Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-827730-2 Glencoe Algebra 1Chapter 6 Resource Masters
3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04
Glencoe/McGraw-Hill
CONSUMABLE WORKBOOKS Many of the worksheets contained in the ChapterResource Masters booklets are available as consumable workbooks in bothEnglish and Spanish.
Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7Reading to Learn Mathematics Workbook 0-07-861060-5
ANSWERS FOR WORKBOOKS The answers for Chapter 6 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
StudentWorks™ This CD-ROM includes the entire Student Edition text alongwith the English workbooks listed above.
TeacherWorks™ All of the materials found in this booklet are included for view-ing and printing in the Glencoe Algebra 1 TeacherWorks CD-ROM.
© Glencoe/McGraw-Hill iii Glencoe Algebra 1
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 6-1Study Guide and Intervention . . . . . . . . 343–344Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 345Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 346Reading to Learn Mathematics . . . . . . . . . . 347Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 348
Lesson 6-2Study Guide and Intervention . . . . . . . . 349–350Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 351Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 352Reading to Learn Mathematics . . . . . . . . . . 353Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 354
Lesson 6-3Study Guide and Intervention . . . . . . . . 355–356Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 357Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 358Reading to Learn Mathematics . . . . . . . . . . 359Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 360
Lesson 6-4Study Guide and Intervention . . . . . . . . 361–362Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 363Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 364Reading to Learn Mathematics . . . . . . . . . . 365Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 366
Lesson 6-5Study Guide and Intervention . . . . . . . . 367–368Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 369Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 370Reading to Learn Mathematics . . . . . . . . . . 371Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 372
Lesson 6-6Study Guide and Intervention . . . . . . . . 373–374Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 375Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 376Reading to Learn Mathematics . . . . . . . . . . 377Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 378
Chapter 6 AssessmentChapter 6 Test, Form 1 . . . . . . . . . . . . 379–380Chapter 6 Test, Form 2A . . . . . . . . . . . 381–382Chapter 6 Test, Form 2B . . . . . . . . . . . 383–384Chapter 6 Test, Form 2C . . . . . . . . . . . 385–386Chapter 6 Test, Form 2D . . . . . . . . . . . 387–388Chapter 6 Test, Form 3 . . . . . . . . . . . . 389–390Chapter 6 Open-Ended Assessment . . . . . . 391Chapter 6 Vocabulary Test/Review . . . . . . . 392Chapter 6 Quizzes 1 & 2 . . . . . . . . . . . . . . . 393Chapter 6 Quizzes 3 & 4 . . . . . . . . . . . . . . . 394Chapter 6 Mid-Chapter Test . . . . . . . . . . . . 395Chapter 6 Cumulative Review . . . . . . . . . . . 396Chapter 6 Standardized Test Practice . . 397–398First Semester Test (Ch. 1–6) . . . . . . . . 399–402
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A31
© Glencoe/McGraw-Hill iv Glencoe Algebra 1
Teacher’s Guide to Using theChapter 6 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 6 Resource Masters includes the core materials neededfor Chapter 6. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 6-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Algebra 1
Assessment OptionsThe assessment masters in the Chapter 6Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 364–365. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
66
© Glencoe/McGraw-Hill vii Glencoe Algebra 1
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 6.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
Addition Property of Inequalities
boundary
compound inequality
Division Property of Inequalities
half-plane
intersection
Multiplication Property of Inequalities
(continued on the next page)
© Glencoe/McGraw-Hill viii Glencoe Algebra 1
Vocabulary Term Found on Page Definition/Description/Example
set-builder notation
Subtraction Property of Inequalities
union
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
66
Study Guide and InterventionSolving Inequalities by Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
6-16-1
© Glencoe/McGraw-Hill 343 Glencoe Algebra 1
Less
on
6-1
Solve Inequalities by Addition Addition can be used to solve inequalities. If anynumber is added to each side of a true inequality, the resulting inequality is also true.
Addition Property of InequalitiesFor all numbers a, b, and c, if a � b, then a � c � b � c, and if a � b, then a � c � b � c.
The property is also true when � and � are replaced with � and �.
Solve x � 8 � �6.Then graph it on a number line.
x � 8 � �6 Original inequality
x � 8 � 8 � �6 � 8 Add 8 to each side.
x � 2 Simplify.
The solution in set-builder notation is {x|x � 2}.Number line graph:
�4 �3 �2 �1 0 1 2 3 4
Solve 4 � 2a � �a. Thengraph it on a number line.
4 � 2a � �a Original inequality
4 � 2a � 2a � �a � 2a Add 2a to each side.
4 � a Simplify.
a � 4 4 � a is the same as a � 4.
The solution in set-builder notation is {a|a � 4}.Number line graph:
�2 �1 0 1 2 3 4 5 6
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each inequality. Then check your solution, and graph it on a number line.
1. t � 12 � 16 2. n � 12 � 6 3. 6 � g � 3
4. n � 8 � �13 5. �12 � �12 � y 6. �6 � s � 8
Solve each inequality. Then check your solution.
7. �3x � 8 � 4x 8. 0.6n � 12 � 0.4n 9. �8k � 12 � � 9k
10. �y � 10 � 15 � 2y 11. z � � 12. �2b � �4 � 3b
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
13. A number decreased by 4 is less than 14.
14. The difference of two numbers is more than 12, and one of the numbers is 3.
15. Forty is no greater than the difference of a number and 2.
4�3
1�3
�4 �2 �1 0 1 2 3�3 4�3�4 �2 �1 0 1 2 3 4�9�10 �8 �7 �6 �5 �4 �3 �2
7 8 9 10 11 12 13 14 1514 1512 13 16 17 18 19 2026 27 28 29 30 31 32 33 34
© Glencoe/McGraw-Hill 344 Glencoe Algebra 1
Solve Inequalities by Subtraction Subtraction can be used to solve inequalities. If anynumber is subtracted from each side of a true inequality, the resulting inequality is also true.
Subtraction Property of InequalitiesFor all numbers a, b, and c, if a � b, then a � c � b � c, and if a � b, then a � c � b � c.
The property is also true when � and � are replaced with � and �.
Solve 3a � 5 � 4 � 2a. Then graph it on a number line.
3a � 5 � 4 � 2a Original inequality
3a � 5 � 2a � 4 � 2a � 2a Subtract 2a from each side.
a � 5 � 4 Simplify.
a � 5 � 5 � 4 � 5 Subtract 5 from each side.
a � �1 Simplify.
The solution is {aa � �1}.Number line graph:
Solve each inequality. Then check your solution, and graph it on a number line.
1. t � 12 � 8 2. n � 12 � �12 3. 16 � h � 9
4. y � 4 � � 2 5. 3r � 6 � 4r 6. q � 5 � q
Solve each inequality. Then check your solution.
7. 4p � 3p � 0.7 8. r � � 9. 9k � 12 � 8k
10. � 1.2 � 2.4 � y 11. 4y � 5y� 14 12. 3n � 17 � 4n
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
13. The sum of a number and 8 is less than 12.
14. The sum of two numbers is at most 6, and one of the number is �2.
15. The sum of a number and 6 is greater than or equal to �4.
3�8
1�4
210 3 4 5 6 7 82 3 4 5 6 7 91 8�8 �7 �6 �5 �4 �3 �2 �1 0
1�2
3�2
5 6 7 8 9 10 11 12 13�26 �25 �24 �23 �22 �21�6 �5 �4 �3 �2 �1 0 1 2
�4 �3 �2 �1 0 1 2 3 4
Study Guide and Intervention (continued)
Solving Inequalities by Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
6-16-1
ExampleExample
ExercisesExercises
Skills PracticeSolving Inequalities by Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
6-16-1
© Glencoe/McGraw-Hill 345 Glencoe Algebra 1
Less
on
6-1
Match each inequality with its corresponding graph.
1. x � 11 � 16 a.
2. x � 6 � 1 b.
3. x � 2 � �3 c.
4. x � 3 � 1 d.
5. x � 1 � �7 e.
Solve each inequality. Then check your solution, and graph it on a number line.
6. d � 5 � 1 7. s � 9 � 8
8. a � 7 � �13 9. w � 1 � 4
10. 4 � k � 3 11. �9 � b � 4
12. �2 � x � 4 13. 2y � y � 2
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
14. A number decreased by 10 is greater than �5.
15. A number increased by 1 is less than 9.
16. Seven more than a number is less than or equal to �18.
17. Twenty less than a number is at least 15.
18. A number plus 2 is at most 1.
�2 �1�4 �3 0 1 2 3 4�6 �5�8 �7 �4 �3 �2 �1 0
�8 �7 �6 �5 �4 �3 �2 �1 0�2 �1�4 �3 0 1 2 3 4
2 30 1 4 5 6 7 8�8 �7 �6 �5 �4 �3 �2 �1 0
�2 �1�4 �3 0 1 2 3 42 30 1 4 5 6 7 8
0 1 2 3 4 5 6 7 8
�8 �7 �6 �5 �4 �3 �2 �1 0
876543210
43210�1�2�3�4
�8 �7 �6 �5 �4 �3 �2 �1 0
© Glencoe/McGraw-Hill 346 Glencoe Algebra 1
Match each inequality with its corresponding graph.
1. �8 � x � 15 a.
2. 4x � 3 � 5x b.
3. 8x � 7x � 4 c.
4. 12 � x � 9 d.
Solve each inequality. Then check your solution, and graph it on a number line.
5. r � (�5) � �2 6. 3x � 8 � 4x
7. n � 2.5 � �5 8. 1.5 � y � 1
9. z � 3 � 10. � c �
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
11. The sum of a number and 17 is no less than 26.
12. Twice a number minus 4 is less than three times the number.
13. Twelve is at most a number decreased by 7.
14. Eight plus four times a number is greater than five times the number.
15. ATMOSPHERIC SCIENCE The troposphere extends from the earth’s surface to a heightof 6–12 miles, depending on the location and the season. If a plane is flying at analtitude of 5.8 miles, and the troposphere is 8.6 miles deep in that area, how muchhigher can the plane go without leaving the troposphere?
16. EARTH SCIENCE Mature soil is composed of three layers, the uppermost being topsoil.Jamal is planting a bush that needs a hole 18 centimeters deep for the roots. Theinstructions suggest an additional 8 centimeters depth for a cushion. If Jamal wants toadd even more cushion, and the topsoil in his yard is 30 centimeters deep, how muchmore cushion can he add and still remain in the topsoil layer?
�4 �3 �2 �1 0 1 2 3 4�4 �3 �2 �1 0 1 2 3 4
3�4
1�2
2�3
�4 �3 �2 �1 0 1 2 3 4�4 �3 �2 �1 0 1 2 3 4
4 52 3 6 7 8 9 10�8 �7 �6 �5 �4 �3 �2 �1 0
2 3 4 5 6 7 810
�8 �7 �6 �5 �4 �3 �2 �1 0
876543210
210�1�2�3�4�5�6
Practice Solving Inequalities by Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
6-16-1
Reading to Learn MathematicsSolving Inequalities by Addition and Subtraction
NAME ______________________________________________ DATE ____________ PERIOD _____
6-16-1
© Glencoe/McGraw-Hill 347 Glencoe Algebra 1
Less
on
6-1
Pre-Activity How are inequalities used to describe school sports?
Read the introduction to Lesson 6-1 at the top of page 318 in your textbook.
• Use the information in the graph to write an inequality statement aboutparticipation in two sports.
• Rewrite your inequality statement to show that 40 schools added both ofthe sports. Is the statement still true?
Reading the LessonWrite the letter of the graph that matches each inequality.
1. x � �1 a.
2. x � �1 b.
3. x � �1 c.
4. x � �1 d.
5. Use the chart to write a sentence that could be described by the inequality 3n � 2n � 7.Then solve the inequality.
Inequalities
� � � �
less than greater than at most at leastfewer than more than no more than no less than
less than or equal to greater than or equal to
Helping You Remember
6. Teaching someone else can help you remember something. Explain how you would teachanother student who missed class to solve the inequality 2x � 4 � 3x.
3210�1�2�3
3210�1�2�3
�3 �2 �1 0 1 2 3
�3 �2 �1 0 1 2 3
© Glencoe/McGraw-Hill 348 Glencoe Algebra 1
Triangle InequalitiesRecall that a line segment can be named by the letters of its endpoints. Line segment AB (written as A�B�) has points A and B forendpoints. The length of AB is written without the bar as AB.
AB � BC m�A � m�B
The statement on the left above shows that A�B� is shorter than B�C�.The statement on the right above shows that the measure of angle Ais less than that of angle B.
These three inequalities are true for any triangle ABC,no matter how long the sides.
a. AB � BC � ACb. If AB � AC, then m�C � m�B.c. If m�C � m�B, then AB � AC.
Use the three triangle inequalities for these problems.
1. List the sides of triangle DEF in order of increasing length.
2. In the figure at the right, which line segment is the shortest?
3. Explain why the lengths 5 cm, 10 cm, and 20 cm could not be usedto make a triangle.
4. Two sides of a triangle measure 3 in. and 7 in. Between which twovalues must the third side be?
5. In triangle XYZ, XY 15, YZ 12, and XZ 9. Which is thegreatest angle? Which is the least?
6. List the angles �A, �C, �ABC, and �ABD, in order of increasing size. C
A
DB
13
15
12
5
9
JM
K
L
65�
60�65�55�
65�50�
D
F E60� 35�
85�
A
B C
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
6-16-1
Study Guide and InterventionSolving Inequalities by Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
6-26-2
© Glencoe/McGraw-Hill 349 Glencoe Algebra 1
Less
on
6-2
Solve Inequalities by Multiplication If each side of an inequality is multiplied bythe same positive number, the resulting inequality is also true. However, if each side of aninequality is multiplied by the same negative number, the direction of the inequality mustbe reversed for the resulting inequality to be true.
For all numbers a, b, and c, with c 0,
1. if c is positive and a � b, then ac � bc;Multiplication Property of Inequalities if c is positive and a � b, then ac � bc;
2. if c is negative and a � b, then ac � bc;if c is negative and a � b, then ac � bc.
The property is also true when � and � are replaced with � and �.
Solve � � 12.
� � 12 Original equation
(�8)�� � � (�8)12 Multiply each side by �8; change � to �.
y � �96 Simplify.
The solution is {yy � �96}.
y�8
y�8
y8
Solve k � 15.
k � 15 Original equation
� � k � � �15 Multiply each side by .
k � 20 Simplify.
The solution is {kk � 20}.
4�3
4�3
3�4
4�3
3�4
34
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each inequality. Then check your solution.
1. � 2 2. � � 22 3. h � �3 4. � � �6
5. n � 10 6. � b � 7. � � 8. �2.51 � �
9. � �2 10. � � � 11. � 5.4 12. � �6
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
13. Half of a number is at least 14.
14. The opposite of one-third a number is greater than 9.
15. One fifth of a number is at most 30.
2a�7
n�10
9p�5
3�4
g�5
2h�4
3�20
3m�5
1�3
2�3
1�4
p�6
3�5
n�50
y�6
© Glencoe/McGraw-Hill 350 Glencoe Algebra 1
Solve Inequalities by Division If each side of a true inequality is divided by thesame positive number, the resulting inequality is also true. However, if each side of aninequality is divided by the same negative number, the direction of the inequality symbolmust be reversed for the resulting inequality to be true.
For all numbers a, b, and c with c 0,
Division Property 1. if c is positive and a � b, then � ; if c is positive and a � b, then � ;of Inequalities
2. if c is negative and a � b, then � ; if c is negative and a � b, then � .
The property is also true when � and � are replaced with � and �.
Solve �12y � 48.
�12y � 48 Original inequality
� Divide each side by �12 and change � to �.
y � �4 Simplify.
The solution is { yy � �4}.
Solve each inequality. Then check your solution.
1. 25g � �100 2. �2x � 9 3. �5c � 2 4. �8m � �64
5. �6k � 6. 18 � �3b 7. 30 � �3n 8. �0.24� 0.6w
9. 25 � �2m 10. �30 � �5p 11. �2n � 6.2 12. �35 � 0.05h
13. �40 � 10h 14. � n � 6 15. �3 �
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
16. Four times a number is no more than 108.
17. The opposite of three times a number is greater than 12.
18. Negative five times a number is at most 100.
p�4
2�3
1�5
48��12
�12y��12
b�c
a�c
b�c
a�c
b�c
a�c
b�c
a�c
Study Guide and Intervention (continued)
Solving Inequalities by Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
6-26-2
ExampleExample
ExercisesExercises
Skills PracticeSolving Inequalities by Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
6-26-2
© Glencoe/McGraw-Hill 351 Glencoe Algebra 1
Less
on
6-2
Match each inequality with its corresponding statement.
1. 3n � 9 a. Three times a number is at most nine.
2. n � 9 b. One third of a number is no more than nine.
3. 3n � 9 c. Negative three times a number is more than nine.
4. �3n � 9 d. Three times a number is less than nine.
5. n � 9 e. Negative three times a number is at least nine.
6. �3n � 9 f. One third of a number is greater than or equal to nine.
Solve each inequality. Then check your solution.
7. 14g � 56 8. 11w � 77 9. 20b � �120 10. �8r � 16
11. �15p � �90 12. � 9 13. � �15 14. � � �9
15. � � 6 16. 5z � �90 17. �13m � �26 18. � �17
19. �y � 36 20. �16c � �224 21. � � 2 22. 12 �
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
23. Four times a number is greater than �48.
24. One eighth of a number is less than or equal to 3.
25. Negative twelve times a number is no more than 84.
26. Negative one sixth of a number is less than �9.
27. Eight times a number is at least 16.
d�12
h�10
k�5
t�12
p�7
a�9
s�4
1�3
1�3
© Glencoe/McGraw-Hill 352 Glencoe Algebra 1
Match each inequality with its corresponding statement.
1. �4n � 5 a. Negative four times a number is less than five.
2. n � 5 b. Four fifths of a number is no more than five.
3. 4n � 5 c. Four times a number is fewer than five.
4. n � 5 d. Negative four times a number is no less than five.
5. 4n � 5 e. Four times a number is at most five.
6. �4n � 5 f. Four fifths of a number is more than five.
Solve each inequality. Then check your solution.
7. � � �14 8. �13h � 52 9. � �6 10. 39 � 13p
11. n � �12 12. � t � 25 13. � m � �6 14. k � �10
15. �3b � 0.75 16. �0.9c � �9 17. 0.1x � �4 18. �2.3 �
19. �15y � 3 20. 2.6v � �20.8 21. 0 � �0.5u 22. f � �1
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
23. Negative three times a number is at least 57.
24. Two thirds of a number is no more than �10.
25. Negative three fifths of a number is less than �6.
26. FLOODING A river is rising at a rate of 3 inches per hour. If the river rises more than 2feet, it will exceed flood stage. How long can the river rise at this rate without exceedingflood stage?
27. SALES Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. If thestore wants to make a profit of no less than $5225, how many bags of dog food does itneed to sell?
7�8
j�4
10�3
3�5
5�9
2�3
s�16
a�5
4�5
4�5
Practice Solving Inequalities by Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
6-26-2
Reading to Learn MathematicsSolving Inequalities by Multiplication and Division
NAME ______________________________________________ DATE ____________ PERIOD _____
6-26-2
© Glencoe/McGraw-Hill 353 Glencoe Algebra 1
Less
on
6-2
Pre-Activity Why are inequalities important in landscaping?
Read the introduction to Lesson 6-2 at the top of page 325 in your textbook.
• Would a wall 6 bricks high be lower than a wall 6 blocks high? Why?
• Would a wall n bricks high be lower than a wall n blocks high? Explain.
Reading the Lesson
1. Write an inequality that describes each situation.
a. A number n divided by 8 is greater than 5.
b. Twelve times a number k is at least 7.
c. A number x divided by �10 is less than or equal to 50.
d. Three fifths of a number n is at most 13.
e. Nine is greater than or equal to one half of a quantity m.
2. Use words to tell what each inequality says.
a. 12 � 6n
b. � 14
c. 11x � 32
Helping You Remember
3. In your own words, write a rule for multiplying and dividing inequalities by positive andnegative numbers.
t��3
© Glencoe/McGraw-Hill 354 Glencoe Algebra 1
The Maya 'I'he Maya were a Native American people who lived from about1500 B.C. to about 1500 A.D. in the region that today encompassesmuch of Central America and southern Mexico. Their manyaccomplishments include exceptional architecture, pottery,painting, and sculpture, as well as significant advances in thefields of astronomy and mathematics.
The Maya developed a system of numeration that was based onthe number twenty. The basic symbols of this system are shown inthe table at the right. The places in a Mayan numeral are writtenvertically—the bottom place represents ones, the place aboverepresents twenties, the place above that represents 20 � 20, orfour hundreds, and so on. For instance, this is how to write thenumber 997 in Mayan numerals.
← 2 � 800
← 9 � 180
← 17 � 17997
Evaluate each expression when v , w , x , y , and z . Then write the answer in Mayan numerals. Exercise 5 is done for you.
1. 2. 3. xv
4. vxy 5. wx � z 6. vz � xy
7. w(v � x � z) 8. vwz 9. z(wx � x)
Tell whether each statement is true or false.
10. � � 11. 12.
13. ( � ) � � ( � )
14. How are Exercises 10 and 11 alike? How are they different?
_______________• • •_______________• • •
• • •____________________
• • •_______________
•_____
• • •__________
• • •__________
•_____• • •__________•_____•_____• • •__________
●●●●
• • •
●●●●
●●●●
v � w � z��x
z�w
• •__________●●●●• • • •• • • _______________•_____
1• •_______________
20• • • •_____
400• •
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
6-26-2
0 10
1 11
2 12
3 13
4 14
5 15
6 16
7 17
8 18
9 19 • • • •_______________• • • •_____
• • • _______________• • •_____
• •_______________• •_____
•_______________•_____
____________________
• • • •__________• • • •
• • •__________• • •
• •__________• •
•__________•
__________●●●●
Study Guide and InterventionSolving Multi-Step Inequalities
NAME ______________________________________________ DATE ____________ PERIOD _____
6-36-3
© Glencoe/McGraw-Hill 355 Glencoe Algebra 1
Less
on
6-3
Solve Multi-Step Inequalities To solve linear inequalities involving more than oneoperation, undo the operations in reverse of the order of operations, just as you would solvean equation with more than one operation.
Solve 6x � 4 � 2x � 12.
6x � 4 � 2x � 12 Original inequality
6x � 4 � 2x � 2x � 12 � 2x Subtract 2x from
each side.
4x � 4 � 12 Simplify.
4x � 4 � 4 � 12 � 4 Add 4 to each side.
4x � 16 Simplify.
� Divide each side by 4.
x � 4 Simplify.
The solution is {xx � 4}.
16�4
4x�4
Solve 3a � 15 � 4 � 5a.
3a � 15 � 4 � 5a Original inequality
3a � 15 � 5a � 4 � 5a � 5a Subtract 5a from
each side.
�2a � 15 � 4 Simplify.
�2a � 15 � 15 � 4 � 15 Add 15 to each side.
�2a � 19 Simplify.
�Divide each side by �2
and change � to �.
a � �9 Simplify.
The solution is �aa � �9 �.1�2
1�2
19��2
�2a��2
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each inequality. Then check your solution.
1. 11y � 13 � �1 2. 8n � 10 � 6 � 2n 3. � 1 � �5
4. 6n � 12 � 8 � 8n 5. �12 � d � �12 � 4d 6. 5r � 6 � 8r � 18
7. � 12 8. 7.3y � 14.4 � 4.9y 9. �8m � 3 � 18 � m
10. �4y � 10 � 19 � 2y 11. 9n � 24n � 45 � 0 12. � �4
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
13. Negative three times a number plus four is no more than the number minus eight.
14. One fourth of a number decreased by three is at least two.
15. The sum of twelve and a number is no greater than the sum of twice the number and �8.
4x � 2�5
�3x � 6��2
q�7
© Glencoe/McGraw-Hill 356 Glencoe Algebra 1
Solve Inequalities Involving the Distributive Property When solvinginequalities that contain grouping symbols, first use the Distributive Property to remove thegrouping symbols. Then undo the operations in reverse of the order of operations, just as youwould solve an equation with more than one operation.
Solve 3a � 2(6a � 4) � 4 � (4a � 6).
3a � 2(6a � 4) � 4 � (4a � 6) Original inequality
3a � 12a � 8 � 4 � 4a � 6 Distributive Property
�9a � 8 � �2 � 4a Combine like terms.
�9a � 8 � 4a � �2 � 4a � 4a Add 4a to each side.
�5a � 8 � �2 Combine like terms.
�5a � 8 � 8 � �2 � 8 Subtract 8 from each side.
�5a � �10 Simplify.
a � 2 Divide each side by �5 and change � to �.
The solution in set-builder notation is {aa � 2}.
Solve each inequality. Then check your solution.
1. 2(t � 3) � 16 2. 3(d � 2) � 2d � 16 3. 4h � 8 � 2(h � 1)
4. 6y � 10 � 8 � (y � 14) 5. 4.6(x � 3.4) � 5.1x 6. �5x � (2x � 3) � 1
7. 3(2y � 4) � 2(y � 1) � 10 8. 8 � 2(b � 1) � 12 � 3b 9. �2(k � 1) � 8(1� k)
10. 0.3( y � 2) � 0.4(1 � y) 11. m � 17 � �(4m � 13)
12. 3n � 8 � 2(n � 4) � 2(1 � n) 13. 2(y � 2) � �4 � 2y
14. k � 17 � �(17 � k) 15. n � 4 � � 3(2 � n)
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
16. Twice the sum of a number and 4 is less than 12.
17. Three times the sum of a number and six is greater than four times the numberdecreased by two.
18. Twice the difference of a number and four is less than the sum of the number and five.
Study Guide and Intervention (continued)
Solving Multi-Step Inequalities
NAME ______________________________________________ DATE ____________ PERIOD _____
6-36-3
ExampleExample
ExercisesExercises
Skills PracticeSolving Multi-Step Inequalities
NAME ______________________________________________ DATE ____________ PERIOD _____
6-36-3
© Glencoe/McGraw-Hill 357 Glencoe Algebra 1
Less
on
6-3
Justify each indicated step.
1. t � 3 � �15
t � 3 � 3 � �15 � 3 a.
t � �12
� �t � (�12) b.
t � �16
2. 5(k � 8) � 7 � 235k � 40 � 7 � 23 a.
5k � 33 � 235k � 33 � 33 � 23 � 33 b.
5k � �10
� c.
k � �2
?�10�5
5k�5
?
?
?4�3
3�4
4�3
3�4
?3�4
3�4
Solve each inequality. Then check your solution.
3. �2b � 4 � �6 4. 3x � 15 � 21 5. � 1 � 3
6. a � 4 � 2 7. � � 7 � �4 8. j � 10 � 5
9. � f � 3 � �9 10. 2p � 5 � 3p � 10 11. 4k � 15 � �2k � 3
12. 2(�3m � 5) � �28 13. �6(w � 1) � 2(w � 5) 14. 2(q � 3) � 6 � �10
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
15. Four more than the quotient of a number and three is at least nine.
16. The sum of a number and fourteen is less than or equal to three times the number.
17. Negative three times a number increased by seven is less than negative eleven.
18. Five times a number decreased by eight is at most ten more than twice the number.
19. Seven more than five sixths of a number is more than negative three.
20. Four times the sum of a number and two increased by three is at least twenty-seven.
2�3
3�4
t�5
2�5
d�2
© Glencoe/McGraw-Hill 358 Glencoe Algebra 1
Justify each indicated step.
Practice Solving Multi-Step Inequalities
NAME ______________________________________________ DATE ____________ PERIOD _____
6-36-3
1. x �
8x � (8) a.
8x � 5x � 128x � 5x � 5x � 12 � 5x b.
3x � �12
� c.
x � �4
2. 2(2h � 2) � 2(3h � 5) � 124h � 4 � 6h � 10 � 12 a.4h � 4 � 6h � 2
4h � 4 � 6h � 6h � 2 � 6h b.�2h � 4 � �2
�2h � 4 � 4 � �2 � 4 c.�2h � �6
� d.
h � 3
?�6��2
�2h��2
?
?
?
?�12�3
3x�3
?
?5x � 12�8
5x � 12�8
Solve each inequality. Then check your solution.
3. �5 � � �9 4. 4u � 6 � 6u � 20 5. 13 � a � 1
6. � �8 7. � 7
8. h � 9. 3(z � 1) � 11 � �2(z � 13)
10. 3e � 2(4e � 2) � 2(6e � 1) 11. 5n � 3(n � 6) � 0
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
12. A number is less than one fourth the sum of three times the number and four.
13. Two times the sum of a number and four is no more than three times the sum of thenumber and seven decreased by four.
14. GEOMETRY The area of a triangular garden can be no more than 120 square feet. Thebase of the triangle is 16 feet. What is the height of the triangle?
15. MUSIC PRACTICE Nabuko practices the violin at least 12 hours per week. Shepractices for three fourths of an hour each session. If Nabuko has already practiced 3 hours in one week, how many sessions remain to meet or exceed her weekly practice goal?
6h � 3�5
3f � 10�5
w � 3�2
2�3
t�6
Reading to Learn MathematicsSolving Multi-Step Inequalities
NAME ______________________________________________ DATE ____________ PERIOD _____
6-36-3
© Glencoe/McGraw-Hill 359 Glencoe Algebra 1
Less
on
6-3
Pre-Activity How are linear inequalities used in science?
Read the introduction to Lesson 6-3 at the top of page 332 in your textbook.Then write an inequality that could be used to find the temperatures indegrees Celsius for which each substance is a gas.
Argon: Bromine:
Reading the Lesson
1. What does the phrase “undoing the operations in reverse of the order of operations” mean?
2. Describe how checking the solution of an inequality is different from checking thesolution of an equation.
3. Describe how the Distributive Property can be used to remove the grouping symbols inthe inequality 4x � 7(2x � 8) � 3x � 5.
4. Is it possible to have no solution when you solve an inequality? Explain your answer andgive an example.
Helping You Remember
5. Make a checklist of steps you can use when solving inequalities.
© Glencoe/McGraw-Hill 360 Glencoe Algebra 1
Carlos Montezuma During his lifetime, Carlos Montezuma (1865?–1923) was one of themost influential Native Americans in the United States. He wasrecognized as a prominent physician and was also a passionate advocateof the rights of Native American peoples. The exercises that follow willhelp you learn some interesting facts about Dr. Montezuma’s life.
Solve each inequality. The word or phrase next to the equivalent inequality will complete the statement correctly.
1. �2k � 10 2. 5 � r � 9 Montezuma was born in the state He was a Native American of the of . Yavapais, who are a people.
a. k � �5 Arizona a. r � �4 Navajo
b. k � �5 Montana b. r � �4 Mohawk
c. k � 12 Utah c. r � 14 Mohave-Apache
3. �y � �9 4. �3 � q � 12 Montezuma received a medical As a physician, Montezuma's field of degree from in 1889. specialization was .
a. y � 9 Chicago Medical College a. q � �4 heart surgery
b. y � �9 Harvard Medical School b. q � 15 internal medicine
c. y � 9 Johns Hopkins University c. q � �15 respiratory diseases
5. 5 � 4x � 14 � x 6. 7 � t � 7 � tFor much of his career, he maintained In addition to maintaining his medicala medical practice in . practice, he was also a(n) .
a. x � 9 New York City a. t � 7 director of a blood bank
b. x � 3 Chicago b. t � 0 instructor at a medical college
c. x � �9 Boston c. t � �7 legal counsel to physicians
7. 3a � 8 � 4a � 10 8. 6n � 8n � 12 Montezuma founded, wrote, and Montezuma testified before a edited , a monthly newsletter committee of the United States that addressed Native American Congress concerning his work in concerns. treating .
a. a � �2 Yavapai a. n � 6 appendicitis
b. a � 18 Apache b. n � �6 asthma
c. a � 18 Wassaja c. n � �10 heart attacks
?
?
??
??
??
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
6-36-3
Study Guide and InterventionSolving Compound Inequalities
NAME ______________________________________________ DATE ____________ PERIOD _____
6-46-4
© Glencoe/McGraw-Hill 361 Glencoe Algebra 1
Less
on
6-4
Inequalities Containing and A compound inequality containing and is true only ifboth inequalities are true. The graph of a compound inequality containing and is theintersection of the graphs of the two inequalities. Every solution of the compoundinequality must be a solution of both inequalities.
Graph the solutionset of x � 2 and x � �1.
Graph x � 2.
Graph x � �1.
Find the intersection.
The solution set is {x�1 � x � 2}.
�2 �1�3 0 1 2 3
�3 �2 �1 0 1 2 3
�3 �2 �1 0 1 2 3
Solve �1 � x � 2 � 3 usingand. Then graph the solution set.
�1 � x � 2 and x � 2 � 3�1 � 2 � x � 2 � 2 x � 2 � 2 � 3 � 2
�3 � x x � 1
Graph x � �3.
Graph x � 1.
Find the intersection.
The solution set is {x�3 � x � 1}.
�2 �1�4 �3 0 1 2
�3�4 �2 �1 0 1 2
�3�4 �2 �1 0 1 2
Example 1Example 1 Example 2Example 2
ExercisesExercises
Graph the solution set of each compound inequality.
1. b � �1 and b � 3 2. 2 � q � �5 3. x � �3 and x � 4
4. �2 � p � 4 5. �3 � d and d� 2 6. �1 � p � 3
Solve each compound inequality. Then graph the solution set.
7. 4 � w � 3 � 5 8. �3 � p � 5 � 2
9. �4 � x � 2 � �2 10. y � 1� 2 and y � 2 � 1
11. n � 2 � �3 and n � 4 � 6 12. d � 3 � 6d � 12 � 2d � 32
�3 �2 �1 0 1 2 3 4 5�3�4 �2 �1 0 1 2 3 4
�3�4 �2 �1 0 1 2 3 4�7 �6 �5 �4 �3 �2 �1 0 1
0 1 2 3 4 5 6 7 8�3�4 �2 �1 0 1 2 3 4
�3�4 �2 �1 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4�3 �2 �1 0 1 2 3 4 5
�4 �3 �2 �1 0 1 2 3 4�4 �3�6 �5 �2 �1 0 1 2�4 �3 �2 �1 0 1 2 3 4
© Glencoe/McGraw-Hill 362 Glencoe Algebra 1
Inequalities Containing or A compound inequality containing or is true if one orboth of the inequalities are true. The graph of a compound inequality containing or is theunion of the graphs of the two inequalities. The union can be found by graphing bothinequalities on the same number line. A solution of the compound inequality is a solution ofeither inequality, not necessarily both.
Solve 2a � 1 � 11 or a � 3a � 2.
2a � 1 � 11 or a � 3a � 22a � 1 � 1 � 11 � 1 a � 3a � 3a � 3a � 2
2a � 10 �2a � 2
� �
a � 5 a � �1
Graph a � 5.
Graph a � �1.
Find the union.
The solution set is {aa � 5}.
Graph the solution set of each compound inequality.
1. b � 2 or b � �3 2. 3 � q or q � 1 3. y � �4 or y � 0
4. 4 � p or p � 8 5. �3 � d or d � 2 6. �2 � x or 3 � x
Solve each compound inequality. Then graph the solution set.
7. 3 � 3w or 3w � 9 8. �3p � 1 � �11 or p � 2
9. 2x � 4 � 6 or x � 2x � 4 10. 2y � 2 � 12 or y � 3 � 2y
11. n � �2 or 2n � 2 � 6 � n 12. 3a � 2 � 5 or 7 � 3a � 2a � 6
0�1�2�3�4 1 2 3 40�1�2�3�4 1 2 3 4
1�2
0 1 2 3 4 5 6 7 8�2 �1 0 1 2 3 4 5 6
0 1 2 3 4 5 6 7 8�3�4 �2 �1 0 1 2 3 4
�3�4 �2 �1 0 1 2 3 40�1�2�3�4 1 2 3 40�1�2 1 2 3 4 5 6
�3�4�5 �2 �1 0 1 2 3�3�4 �2 �1 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4
�2 �1 0 1 2 3 4 5 6
�2 �1 0 1 2 3 4 5 6
�2 �1 0 1 2 3 4 5 6
2��2
�2a��2
10�2
2a�2
Study Guide and Intervention (continued)
Solving Compound Inequalities
NAME ______________________________________________ DATE ____________ PERIOD _____
6-46-4
ExampleExample
ExercisesExercises
Skills PracticeSolving Compound Inequalities
NAME ______________________________________________ DATE ____________ PERIOD _____
6-46-4
© Glencoe/McGraw-Hill 363 Glencoe Algebra 1
Less
on
6-4
Graph the solution set of each compound inequality.
1. b � 3 or b � 0 2. z � 3 and z � �2
3. k � 1 and k � 5 4. y � �1 or y � 1
Write a compound inequality for each graph.
5. 6.
7. 8.
Solve each compound inequality. Then graph the solution set.
9. m � 3 � 5 and m � 3 � 7 10. y � 5 � �4 or y � 5 � 1
11. 4 � f � 6 and f � 6 � 5 12. w � 3 � 0 or w � 7 � 9
13. �6 � b � 4 � 2 14. p � 2 � �2 or p � 2 � 1
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
15. A number plus one is greater than negative five and less than three.
16. A number decreased by two is at most four or at least nine.
17. The sum of a number and three is no more than eight or is more than twelve.
�3�4 �2 �1 0 1 2 3 4�2 �1 0 1 2 3 4 5 6
�3�4 �2 �1 0 1 2 3 4�4 �3 �2 �1 0 1 2 3 4
�2 �1 0 1 2 3 4 5 6�2 �1 0 1 2 3 4 5 6
�4 �3 �2 �1 0 1 2 3 4�4 �3 �2 �1 0 1 2 3 4
�2 �1 0 1 2 3 4 5 6�2 �1�4 �3 0 1 2 3 4
�3�4 �2 �1 0 1 2 3 40 1 2 3 4 5 6 7 8
�4 �3 �2 �1 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4
© Glencoe/McGraw-Hill 364 Glencoe Algebra 1
Graph the solution set of each compound inequality.
1. �4 � e � 1 2. x � 0 or x � 3
3. g � �3 or g � 4 4. �4 � p � 4
Write a compound inequality for each graph.
5. 6.
7. 8.
Solve each compound inequality. Then graph the solution set.
9. k � 3 � �7 or k � 5 � 8 10. �n � 2 or 2n � 3 � 5
11. 5 � 3h � 2 � 11 12. 2c � 4 � �6 and 3c � 1 � 13
Define a variable, write an inequality, and solve each problem. Then check yoursolution.
13. Two times a number plus one is greater than five and less than seven.
14. A number minus one is at most nine, or two times the number is at least twenty-four.
METEOROLOGY For Exercises 15 and 16, use the following information.Strong winds called the prevailing westerlies blow from west to east in a belt from 40° to60° latitude in both the Northern and Southern Hemispheres.
15. Write an inequality to represent the latitude of the prevailing westerlies.
16. Write an inequality to represent the latitudes where the prevailing westerlies are not located.
17. NUTRITION A cookie contains 9 grams of fat. If you eat no fewer than 4 and no more than7 cookies, how many grams of fat will you consume?
�2 �1 0 1 2 3 4 5 6�2 �1�4 �3 0 1 2 3 4
�4 �3 �2 �1 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4
�2�3�4�5�6 �1 0 1 2�2 �1 0 1 2 3 4 5 6
�2 �1 0 1 2 3 4 5 6�4 �3 �2 �1 0 1 2 3 4
�2 �1�4 �3 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4
0�1�2�3�4 1 2 3 4�2 �1�4 �3�6 �5 0 1 2
Practice Solving Compound Inequalities
NAME ______________________________________________ DATE ____________ PERIOD _____
6-46-4
Reading to Learn MathematicsSolving Compound Inequalities
NAME ______________________________________________ DATE ____________ PERIOD _____
6-46-4
© Glencoe/McGraw-Hill 365 Glencoe Algebra 1
Less
on
6-4
Pre-Activity How are compound inequalities used in tax tables?
Read the introduction to Lesson 6-4 at the top of page 339 in your textbook.
• Explain why it is possible that Mr. Kelly’s income is $41,370.
• Explain why it is not possible that Mr. Kelly’s income is $41,400.
Reading the Lesson
1. When is a compound inequality containing and true?
2. The graph of a compound inequality containing and is the of thegraphs of the two inequalities.
3. When is a compound inequality containing or true?
4. The graph of a compound inequality containing or is the of thegraphs of the two inequalities.
5. Suppose you use yellow to show the graph of Inequality #1 on the number line. You useblue to show the graph of Inequality #2. Write and or or in each blank to complete thesentence.
a. The part that is green is the graph of Inequality #1 Inequality #2.
b. All colored parts form the graph of Inequality #1 Inequality #2.
Helping You Remember
6. One way to remember something is to connect it to something that is familiar to you.Write two true compound statements about yourself, one using the word and and theother using the word or.
© Glencoe/McGraw-Hill 366 Glencoe Algebra 1
Some Properties of InequalitiesThe two expressions on either side of an inequality symbol aresometimes called the first and second members of the inequality.
If the inequality symbols of two inequalities point in the samedirection, the inequalities have the same sense. For example, a � band c � d have the same sense; a � b and c � d have opposite senses.
In the problems on this page, you will explore some properties of inequalities.
Three of the four statements below are true for all numbers aand b (or a, b, c, and d). Write each statement in algebraicform. If the statement is true for all numbers, prove it. If it isnot true, give an example to show that it is false.
1. Given an inequality, a new and equivalent inequality can becreated by interchanging the members and reversing the sense.
2. Given an inequality, a new and equivalent inequality can be createdby changing the signs of both terms and reversing the sense.
3. Given two inequalities with the same sense, the sum of thecorresponding members are members of an equivalent inequalitywith the same sense.
4. Given two inequalities with the same sense, the difference of thecorresponding members are members of an equivalent inequalitywith the same sense.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
6-46-4
Study Guide and InterventionSolving Open Sentences Involving Absolute Value
NAME ______________________________________________ DATE ____________ PERIOD _____
6-56-5
© Glencoe/McGraw-Hill 367 Glencoe Algebra 1
Less
on
6-5
Absolute Value Equations When solving equations that involve absolute value, thereare two cases to consider.Case 1: The value inside the absolute value symbols is positive.Case 2: The value inside the absolute value symbols is negative.
Solve x � 4 1. Thengraph the solution set.
Write x � 4 1 as x � 4 1 or x � 4 �1.
x � 4 1 or x � 4 �1x � 4 � 4 1 � 4 x � 4 �1
x �3 x � 4 � 4 �1� 4x �5
The solution set is {�5, �3}.The graph is shown below.
�8 �7 �6 �5 �4 �3 �2 �1 0
Write an inequalityinvolving absolute value for the graph.
Find the point that is the same distancefrom �2 as it is from 4.
The distance from 1 to �2 is 3 units. Thedistance from 1 to 4 is 3 units.So, x � 1 3.
10�1�2�3 2 3
3 units 3 units
4 5
�3 �2 �1 0 1 2 3 4 5
Example 1Example 1 Example 2Example 2
ExercisesExercises
Solve each open sentence. Then graph the solution set.
1. y 3 2. x � 4 4 3. y � 3 2
4. b � 2 3 5. w � 2 5 6. t � 2 4
7. 2x 8 8. 5y � 2 7 9. p � 0.2 0.5
10. d � 100 50 11. 2x � 1 11 12. 3x � 6
For each graph, write an open sentence involving absolute value.
13. 14. 15.�3�4�5�6�7 �2 �1 0 1�3�4 �2 �1 0 1 2 3 40�2�4�6�8 2 4 6 8
�2�3 �1 0 1 2 3 4 5�4�6 �2 0 2 4 6 8 1050 100 150 200
1�2
�0.8 �0.4 0 0.4 0.8�3�4 �2 �1 0 1 2 3 4�3�4 �2 �1 0 1 2 3 4
�8 �6 �4 �2 0 2 4 6 8�8 �6 �4 �2 0 2 4 6 8�6 �5 �4 �3 �2 �1 0 1 2
�8 �7 �6 �5 �4 �3 �2 �1 00 1 2 3 4 5 6 7 8�3�4 �2 �1 0 1 2 3 4
© Glencoe/McGraw-Hill 368 Glencoe Algebra 1
Absolute Value Inequalities When solving inequalities that involve absolute value, there are two cases to consider for inequalities involving � (or �) and two cases to consider for inequalities involving � (or �).
Remember that inequalities with and are related to intersections, while inequalities with or are related to unions.
Solve |3a � 4| � 10. Then graph the solution set.
Write 3a � 4 � 10 as 3a � 4 � 10 and 3a � 4 � �10.3a � 4 � 10 and 3a � 4 � �10
3a � 4 � 4 � 10 � 4 3a � 4 � 4 � �10 � 43a � 6 3a � �14
� �
a � 2 a � �4
The solution set is �a�4 � a � 2�.
Solve each open sentence. Then graph the solution set.
1. c � 2 � 6 2. x � 9 � 0 3. 3f � 10 � 4
4. x � 2 5. x � 3 6. 2x � 1 � �2
7. 2d � 1 � 4 8. 3 � (x � 1) � 8 9. 3r � 2 � �5
For each graph, write an open sentence involving absolute value.
10. 11. 12.�2 �1�3 0 1 2 3 4 5�4 �3 �2 �1 0 1 2 3 4�4 �3 �2 �1 0 1 2 3 4
�4 �3 �2 �1 0 1 2 3 4�4 �2 0 2 4 6 8 10 12�4 �3 �2 �1 0 1 2 3 4
0�1�2�3�4 1 2 3 40�1�2�3�4 1 2 3 4�4 �3 �2 �1 0 1 2 3 4
�6 �5 �4 �3 �2 �1 0 1 2�4 �3 �2 �1 0 1 2 3 420�2�4�6 4 6 8 10
2�3
2�3
�14�3
3a�3
6�3
3a�3
If x � n, then x � �n and x � n.If x � n, then x � n or x � �n.
Study Guide and Intervention (continued)
Solving Open Sentences Involving Absolute Value
NAME ______________________________________________ DATE ____________ PERIOD _____
6-56-5
ExampleExample
ExercisesExercises
Now graph the solution set.
�2 �1�4�5 �3 0 1 2 3
Skills PracticeSolving Open Sentences Involving Absolute Value
NAME ______________________________________________ DATE ____________ PERIOD _____
6-56-5
© Glencoe/McGraw-Hill 369 Glencoe Algebra 1
Less
on
6-5
Match each open sentence with the graph of its solution set.
1. x � 2 a.
2. x � 5 3 b.
3. x � 2 � 3 c.
4. x � 1 � 4 d.
Express each statement using an inequality involving absolute value. Do not solve.
5. The weatherman predicted that the temperature would be within 3° of 52°F.
6. Serena will make the B team if she scores within 8 points of the team average of 92.
7. The dance committee expects attendance to number within 25 of last year’s 87 students.
Solve each open sentence. Then graph the solution set.
8. s � 1 5 9. c � 3� 1
10. n � 2 � 1 11. t � 6 � 4
12. w � 2 2 13. k � 5 � 4
For each graph, write an open sentence involving absolute value.
14. 15.
16. 17.�2�3�4�5 �1 0 1 2 3 4 5�2�3�4�5 �1 0 1 2 3 4 5
�2�3�4�5�6�7 �1 0 1 2 3�5 �4 �3 �2 �1 0 1 2 3 4 5
0 1 2 3 4 5 6 7 8 9 10�3�4 �2 �1 0 1 2 3 4 5 6
�8 �7�10 �9 �6 �5 �4 �3 �2 �1 0�2 �1�4�5�6 �3 0 1 2 3 4
�3 �1 0 1 2 3 4 5 6�2 7�3�4�5�6 �2 �1 0 1 2 3 4
�2�3�4 �1 0 1 2 3 4 5 6
�2�3�4�5 �1 0 1 2 3 4 5
�2�3�4�5 �1 0 1 2 3 4 5
�8�9�10 �7 �6 �5 �4 �3 �2 �1 0
© Glencoe/McGraw-Hill 370 Glencoe Algebra 1
Match each open sentence with the graph of its solution set.
1. x � 7 3 a.
2. x � 3 � 1 b.
3. 2x � 1 � 5 c.
4. 5 � x � 3 d.
Express each statement using an inequality involving absolute value. Do not solve.
5. The height of the plant must be within 2 inches of the standard 13-inch show size.
6. The majority of grades in Sean’s English class are within 4 points of 85.
Solve each open sentence. Then graph the solution set.
7. |2z � 9| � 1 8. |3 � 2r| � 7
9. |3t � 6| � 9 10. |2g � 5| � 9
For each graph, write an open sentence involving absolute value.
11. 12.
13. 14.
15. FITNESS Taisha uses the elliptical cross-trainer at the gym. Her general goal is to burn280 Calories per workout, but she varies by as much as 25 Calories from this amount onany given day. What is the range of the number of Calories burned for Taisha’s cross-trainer workout?
16. TEMPERATURE A thermometer is guaranteed to give a temperature no more than1.2°F from the actual temperature. If the thermometer reads 28°F, what is the range forthe actual temperature?
�2�3 �1 0 1 2 3 4 5 6 7�2�3�4�5�6�7�8 �1 0 1 2
�2�3�4�5�6�7�8 �1 0 1 21 2 3 4 5 6 7 8 9 10 11
�2 �1 0 1 2 3 4 5 6 7 8�5 �4 �3 �2 �1 0 1 2 3 4 5
�5 �4 �3 �2 �1 0 1 2 3 4 5�5 �4 �3 �2 �1 0 1 2 3 4 5
�2�3�4�5 �1 0 1 2 3 4 5
�8�9�10 �7 �6 �5 �4 �3 �2 �1 0
�2 �1 0 1 2 3 4 5 6 7 8
�2�3�4�5 �1 0 1 2 3 4 5
Practice Solving Open Sentences Involving Absolute Value
NAME ______________________________________________ DATE ____________ PERIOD _____
6-56-5
Reading to Learn MathematicsSolving Open Sentences Involving Absolute Value
NAME ______________________________________________ DATE ____________ PERIOD _____
6-56-5
© Glencoe/McGraw-Hill 371 Glencoe Algebra 1
Less
on
6-5
Pre-Activity How is absolute value used in election polls?
Read the introduction to Lesson 6-5 at the top of page 345 in your textbook.
• What does the phrase margin of error mean to you?
• In this poll, the number of people opposed to the tax levy may be as
high as or as low as . This can be written as
the inequality x � � 3.
Reading the Lesson
Complete each compound sentence by writing and or or in the blank. Use theresult to help you graph the absolute value sentence.
Absolute ValueSentence
Compound Sentence Graph
1. 2x � 2 8 2x � 2 8 2x � 2 �8
2. x � 5 � 4 x � 5 � 4 x � 5 � �4
3. 2x � 3 � 5 2x � 3 � 5 2x � 3 � �5
4. How would you write the compound sentence 3x � 7 � 5 or 3x � 7 � �5 as an absolutevalue sentence?
Helping You Remember
5. Recall that x tells you how many units the number x is from zero on the number line.Explain the meaning of x n, x � n, and x � n by using the idea of the distancefrom x to zero.
�2�3 �1 0 1 2 3 4 5 6 7
0 1 2 3 4 5 6 7 8 9 10
�3�4�5�6 �2 �1 0 1 2 3 4
© Glencoe/McGraw-Hill 372 Glencoe Algebra 1
Precision of MeasurementThe precision of a measurement depends both on your accuracy inmeasuring and the number of divisions on the ruler you use. Supposeyou measured a length of wood to the nearest one-eighth of an inch and got a length of 6 in.
The drawing shows that the actual measurement lies somewhere
between 6 in. and 6 in. This measurement can be written using
the symbol �, which is read plus or minus. It can also be written as acompound inequality.
6 � in. 6 in. � m � 6 in.
In this example, in. is the absolute error. The absolute error is
one-half the smallest unit used in a measurement.
Write each measurement as a compound inequality. Use the variable m.
1. 3 � in. 2. 9.78 � 0.005 cm 3. 2.4 � 0.05 g
4. 28 � ft 5. 15 � 0.5 cm 6. � in.
For each measurement, give the smallest unit used and the absolute error.
7. 12.5 cm � m � 13.5 cm 8. 12 in. � m � 12 in.
9. 56 in. � m � 57 in. 10. 23.05 mm � m � 23.15 mm1�2
1�2
3�8
1�8
1�64
11�16
1�2
1�4
1�2
1�16
11�16
9�16
1�16
5�8
11�16
9�11
5 6 7 8
65–8
5�8
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
6-56-5
Study Guide and InterventionGraphing Inequalities in Two Variables
NAME ______________________________________________ DATE ____________ PERIOD _____
6-66-6
© Glencoe/McGraw-Hill 373 Glencoe Algebra 1
Less
on
6-6
Graph Linear Inequalities The solution set of an inequality that involves twovariables is graphed by graphing a related linear equation that forms a boundary of a half-plane. The graph of the ordered pairs that make up the solution set of the inequalityfill a region of the coordinate plane on one side of the half-plane.
Graph y � �3x � 2.
Graph y �3x � 2.Since y � �3x � 2 is the same as y � �3x � 2 and y �3x � 2,the boundary is included in the solution set and the graph should bedrawn as a solid line.Select a point in each half plane and test it. Choose (0, 0) and (�2, �2).
y � �3x � 2 y � �3x � 20 � �3(0) � 2 �2 � �3(�2) � 20 � �2 is false. �2 � 6 � 2
�2 � 4 is true.The half-plane that contains (�2, �2) contains the solution. Shade that half-plane.
Graph each inequality.
1. y � 4 2. x � 1 3. 3x � y
4. �x � y 5. x � y � 1 6. 2x � 3y � 6
7. y � � x � 3 8. 4x � 3y � 6 9. 3x � 6y � 12
x
y
O
x
y
O
x
y
O
1�2
x
y
Ox
y
Ox
y
O
x
y
Ox
y
O
x
y
O
x
y
O
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 374 Glencoe Algebra 1
Solve Real-World Problems When solving real-life inequalities, the domain andrange of the inequality are often restricted to nonnegative numbers or to whole numbers.
BANKING A bank offers 4.5% annual interest on regular savingsaccounts and 6% annual interest on certificates of deposit (CD). If Marjean wantsto earn at least $300 interest per year, how much money should she deposit ineach type of account?
Let x the amount deposited in a regular savings account.Let y the amount deposited in a CD.Then 0.045x � 0.06y � 300 is an open sentence representing this situation.
Solve for y in terms of x.
0.045x � 0.06y � 300 Original inequality
0.06y � �0.045x � 300 Subtract 0.045x from each side.
y � � 0.75x � 5000 Divide each side by 0.06.
Graph y � � 0.75x � 5000 and test the point (0, 0).Since 0 � �0.75(0) � 5000 is false, shade the half-plane that does not contain (0, 0).One solution is (4000, 2000). This represents $4000 deposited at 4.5% and $2,000 deposited at 6%.
1. SOCIAL EVENTS Tickets for the school play cost $5 per student and $7 per adult. The school wants to earn at least $5,400 on each performance.
a. Write an inequality that represents this situation.
b. Graph the solution set.
c. If 500 adult tickets are sold, what is the minimumnumber of student tickets that must be sold?
2. MANUFACTURING An auto parts company can produce 525 four-cylinder engines or270 V-6 engines per day. It wants to produce up to 300,000 engines per year.
a. Write an inequality that represents this situation.
b. Are there restrictions on the domain or range?
3. GEOMETRY The perimeter of a rectangular lot is less than 800 feet. Write aninequality that represents the amount of fencing that will enclose the lot.
Ticket Sales
Student Tickets
Ad
ult
Tic
kets
3000 600 900 x
y
900
600
300
Interest on Accounts
Regular Savings Account ($)C
D A
cco
un
t ($
)
20000 4000 6000 x
y
6000
4000
2000
Study Guide and Intervention (continued)
Graphing Inequalities in Two Variables
NAME ______________________________________________ DATE ____________ PERIOD _____
6-66-6
ExampleExample
ExercisesExercises
Skills PracticeGraphing Inequalities in Two Variables
NAME ______________________________________________ DATE ____________ PERIOD _____
6-66-6
© Glencoe/McGraw-Hill 375 Glencoe Algebra 1
Less
on
6-6
Determine which ordered pairs are part of the solution set for each inequality.
1. y � 3x, {(1, 5), (1, 0), (�1, 0), (5, 1)}
2. y � x � 3, {(2, �3), (�2, �1), (1, 6), (3, 4)}
3. y � x � 1, {(3, 1), (�2, �4), (4, �2), (�3, 3)}
Match each inequality with its graph.
4. y � 2x � 2 a. b.
5. y � �3x
6. 2y � x � 4
7. x � y � 1
c. d.
Graph each inequality.
8. y � �1 9. y � x � 5 10. y � 3x
11. y � 2x � 4 12. y � x � 3 13. y � x � 1
x
y
Ox
y
Ox
y
O
x
y
O
x
y
O
x
y
O
x
y
Ox
y
O
x
y
O
x
y
O
© Glencoe/McGraw-Hill 376 Glencoe Algebra 1
Determine which ordered pairs are part of the solution set for each inequality.
1. 3x � y � 6, {(4, 3), (�2, 4), (�5, �3), (3, �3)}
2. y � x � 3, {(6, 3), (�3, 2), (3, �2), (4, 3)}
3. 3x � 2y � 5, {(4, �4), (3, 5), (5, 2), (�3, 4)}
Match each inequality with its graph.
4. 5y � 2x � 10 a. b.
5. 3y � 3x � 9
6. y � 2x � 3
7. x � 2y � �6
c. d.
Graph each inequality.
8. 2y � x � �4 9. 2x � 2y � 8 10. 3y � 2x � 3
11. MOVING A moving van has an interior height of 7 feet (84 inches). You have boxes in12 inch and 15 inch heights, and want to stack them as high as possible to fit. Write aninequality that represents this situation.
BUDGETING For Exercises 12 and 13, use the following information.
Satchi found a used bookstore that sells pre-owned videos and CDs. Videos cost $9 each, andCDs cost $7 each. Satchi can spend no more than $35.
12. Write an inequality that represents this situation.
13. Does Satchi have enough money to buy 2 videos and 3 CDs?
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
Practice Graphing Inequalities in Two Variables
NAME ______________________________________________ DATE ____________ PERIOD _____
6-66-6
Reading to Learn MathematicsGraphing Inequalities in Two Variables
NAME ______________________________________________ DATE ____________ PERIOD _____
6-66-6
© Glencoe/McGraw-Hill 377 Glencoe Algebra 1
Less
on
6-6
Pre-Activity How are inequalities used in budgets?
Read the introduction to Lesson 6-6 at the top of page 352 in your textbook.
What do 3 and 4 represent in the terms 3x and 4y?
Reading the Lesson
1. Complete the chart to show which type of line is needed for each symbol.
Symbol Type of Line Boundary Part of Solution?
�
�
�
�
2. If a test point results in a false statement, what do you know about the graph?
3. If a test point results in a true statement, what do you know about the graph?
4. When can the origin not be used as a test point?
Helping You Remember
5. The two-variable inequalities in this lesson can be solved for y in terms of x to get asentence in slope-intercept form. It looks much like a slope-intercept equation, but it hasan inequality symbol instead of an equals sign. For example, 4x � 2y � 5 can be written
as y � �2x � . Explain how to graph an inequality once it is written in slope-intercept
form. Use the idea that greater can mean above and less can mean below.
5�2
© Glencoe/McGraw-Hill 378 Glencoe Algebra 1
Using Equations: Ideal WeightYou can find your ideal weight as follows.
A woman should weigh 100 pounds for the first 5 feet of height and 5 additional pounds for each inch over 5 feet (5 feet 60 inches).A man should weigh 106 pounds for the first 5 feet of height and 6 additional pounds for each inch over 5 feet. These formulas apply topeople with normal bone structures.
To determine your bone structure, wrap your thumb and index fingeraround the wrist of your other hand. If the thumb and finger just touch,you have normal bone structure. If they overlap, you are small-boned.If they don’t overlap, you are large-boned. Small-boned people shoulddecrease their calculated ideal weight by 10%. Large-boned peopleshould increase the value by 10%.
Calculate the ideal weights of these people.
1. woman, 5 ft 4 in., normal-boned 2. man, 5 ft 11 in., large-boned
3. man, 6 ft 5 in., small-boned 4. you, if you are at least 5 ft tall
For Exercises 5–9, use the following information.
Suppose a normal-boned man is x inches tall. If he is at least 5 feettall, then x � 60 represents the number of inches this man is over 5 feet tall. For each of these inches, his ideal weight is increased by 6 pounds. Thus, his proper weight ( y) is given by the formula y 6(x � 60) � 106 or y 6x � 254. If the man is large-boned, theformula becomes y 6x � 254 � 0.10(6x � 254).
5. Write the formula for the weight of a large-boned man in slope-intercept form.
6. Derive the formula for the ideal weight ( y) of a normal-bonedfemale with height x inches. Write the formula in slope-intercept form.
7. Derive the formula in slope-intercept form for the ideal weight ( y)of a large-boned female with height x inches.
8. Derive the formula in slope-intercept form for the ideal weight ( y)of a small-boned male with height x inches.
9. Find the heights at which normal-boned males and large-bonedfemales would weigh the same.
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
6-66-6
Chapter 6 Test, Form 1
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 379 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1–9, solve each inequality.
1. x � 7 � 3A. {x � x � 10} B. {x � x � �4} C. {x � x � 10} D. {x � x � �4} 1.
2. 3 � t � 1A. {t � t � 4} B. {t � t � 2} C. {t � t � 2} D. {t � t � 4} 2.
3. 17 � a � 7A. {a � a � 10} B. {a � a � �10} C. {a � a � 24} D. {a � a � �24} 3.
4. 3 � �5c
�
A. �c � c � �35�� B. �c � c � �
35�� C. {c � c � 15} D. {c � c � 15} 4.
5. 1 � ��4y�
A. �y � y � ��14�� B. {y � y � �4} C. {y � y � 4} D. {y � y � 3} 5.
6. 5s � �25A. {s � s � 125} B. {s � s � �125} C. {s � s � �5} D. {s � s � �5} 6.
7. �36 � 3tA. {t � t � �12} B. {t � t � 12} C. {t � t � 12} D. {t � t � �12} 7.
8. 6y � 8 � 4y � 26A. {y � y � �9} B. {y � y � �17} C. {y � y � 9} D. {y � y � 17} 8.
9. 3(2d � 1) � 4(2d � 3) � 3A. {d � d � �9} B. {d � d � �6} C. {d � d � 3} D. {d � d � 6} 9.
10. Six is at least four more than a number. Which inequality represents this sentence?A. 6 � n � 4 B. 6 � n � 4 C. 4 � n � 6 D. 4 � n � 6 10.
11. Which of the following is the graph of the solution set of m � �1 and m � 1?A. B.
C. D. 11.
12. Which compound inequality has the solution set shown in the graph?
A. �3 � n � 1 B. �3 � n � 1 C. �3 � n � 1 D. �3 � n � 1 12.
�1�2�3�4 0 1 2 43
�1�2�3�4 0 1 2 43�1�2�3�4 0 1 2 43
�1�2�3�4 0 1 2 43�1�2�3�4 0 1 2 43
66
© Glencoe/McGraw-Hill 380 Glencoe Algebra 1
Chapter 6 Test, Form 1 (continued)
13. Which compound inequality has the solution set shown in the graph?
A. x � �1 or x � 3 B. x � �1 or x � 3C. x � �1 or x � 3 D. x � �1 or x � 3 13.
14. Which of the following is the solution set of 2s � 1 � 9 or s � �1?A. {s � s � �1 or s � 4} B. {s � s � �1 or s � 4}C. {s � �1 � s � 4} D. {s � s � �1 or s � 5} 14.
15. Which of the following is the solution set of � s � 6 � 12?A. {6, �18} B. {�6} C. {18} D. {�6, 18} 15.
16. Solve � 1 � 2b � 1.A. {1, �1} B. {�1, 0} C. {0, 1} D. {0} 16.
17. Solve � x � 3 � � 2.A. {x � 1 � x � 5} B. {x � �5 � x � �1}C. {x � �1 � x � 1} D. {x � �1 � x � 5} 17.
18. Which inequality has the solution set shown in the graph? A. y � 1 B. y � 1C. y � 1 D. y � 1 18.
19. Which inequality has the solution set shown in the graph?A. y � �x � 2 B. y � �x � 2C. y � �x � 1 D. y � �x � 1 19.
20. Juan’s income y consists of at least $37,500 salary plus 5% commission on all of his sales x. Which inequality represents Juan’s income in one year?A. y � 37,500 � 5x B. y � 37,500 � 0.05xC. y � x � 0.05(37,500) D. y � 37,500 � 5 20.
Bonus If x � 0, which integer does not satisfy the inequality B:x � 2 � 1?
�1�2�3�4 0 1 2 43
NAME DATE PERIOD
66
y
xO
y
xO
(0, 2)
(2, 0)
Chapter 6 Test, Form 2A
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 381 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1–9, solve each inequality.
1. �51 � x � 38A. {x � x � �13} B. {x � x � 89} C. {x � x � �89} D. {x � x � �13} 1.
2. m � �38� � �
12�
A. �m � m � �78�� B. �m � m � �
78�� C. �m � m � �
18�� D. �m � m � �
18�� 2.
3. 6n � 19 � 5n
A. {n � n � �19} B. {n � n � 19} C. {n � n � 19} D. �n � n � �1191�� 3.
4. ��t2�
� 4
A. {t � t � �8} B. {t � t � �2} C. {t � t � 2} D. {t � t � �8} 4.
5. �154�
� ��27�d
A. �d � d � �54�� B. �d � d � �
54�� C. �d � d � ��
54�� D. �d � d � ��
54�� 5.
6. �3.5z � 42A. {z � z � 12} B. {z � z � 12} C. {z � z � �12} D. {z � z � �12} 6.
7. 4w � 6 � 6w � 20A. {w � w � 7} B. {w � w � 2} C. {w � w � �7} D. {w � w � �2} 7.
8. 2v � 3 � �5v
4� 8�
A. �v � v � 1�23�� B. �v � v � �1�
13�� C. �v � v � 1�
23�� D. �v � v � �1�
13�� 8.
9. 8r � (5r � 4) � �31A. {r � r � �9} B. {r � r � �9} C. {r � r � 9} D. {r � r � 9} 9.
10. The sum of two consecutive integers is at most 3. What is the greatest possible value for the greater integer?A. 5 B. 1 C. 3 D. 2 10.
11. Which of the following is the graph of the solution set of y � �3 or y � 1? A. B.
C. D. 11.�1�2�3�4 0 1 2 43�1�2�3�4 0 1 2 43
�1�2�3�4 0 1 2 43�1�2�3�4 0 1 2 43
66
© Glencoe/McGraw-Hill 382 Glencoe Algebra 1
Chapter 6 Test, Form 2A (continued)
12. Which compound inequality has the solution set shown in the graph?
A. �1 � n � 2 B. �1 � n � 2C. n � �1 or n � 2 D. �1 � n � 2 12.
13. Which of the following is the solution set of �4 � 3t � 5 � 20?A. {t ��3 � t � 5} B. {t � t � �3}C. {t � t � �3 and t � 5} D. {t � t � �3 or t � 5} 13.
14. Which of the following is the graph of the solution set of t � 4 � 4t � 8 or 3t � 14 � 4t?A. B.
C. D. 14.
15. Which of the following is the solution set of � 3x � 18 � 12?A. {2} B. {2, 10} C. {�10, �2} D. {10} 15.
16. The graph below represents the solution set of which inequality?
A. � w � 5 � � 3 B. � w � 5 � � 3C. � w � 5 � � 3 D. � w � 5 � � 3 16.
17. Which of the following is the solution set of � 2x � 3 � � 4?
A. �x � x � ��12� or x > �
72�� B. {x � x � �1 or x � 7}
C. �x � ��12� � x � �
72�� D. �x � x � �
12� or x � �
72�� 17.
18. Which ordered pair is part of the solution set of the inequality 12 � y � �3x?A. (�16, 3) B. (1, 4) C. (4, �1) D. (3, �16) 18.
19. Which inequality is graphed at the right?A. y � 2x � 1 B. y � 2x � 1
C. y � �12�x � 1 D. y � �
12�x � 1 19.
20. Taka is planning to buy a new coat and new shoes.He has saved $122. Which inequality represents this situation if x represents the cost of a coat and y represents the cost of the shoes he buys?A. 122 � y � x B. y � 122 � xC. y � x � 122 D. y � 122 � x 20.
Bonus Solve 6(� n � � 3) � 4� n � � 5 11. B:
0 1 2 4 5 6 7 83
�1�2�3�4�5 0 1 2 3�1�2�3�4�5 0 1 2 3
�1�2�3�4�5 0 1 2 3�1�2�3�4�5 0 1 2 3
�1�2�3�4 0 1 2 43
NAME DATE PERIOD
66
y
xO
(0, 1) (2, 2)
Chapter 6 Test, Form 2B
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 383 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1–9, solve each inequality.
1. �13 � w � 12A. {w � w � �25} B. {w � w � �25} C. {w � w � �1} D. {w � w � �1} 1.
2. x � �14� � ��
12�
A. �x � x � ��14�� B. �x � x � ��
34�� C. �x � x � ��
14�� D. �x � x � ��
34�� 2.
3. 2x � 7 � 3x
A. �x � x � �57�� B. {x � x � �7} C. {x � x � 7} D. {x � x � �7} 3.
4. ��m
5�� �3
A. {m � m � �15} B. {m � m � �15} C. {m � m � 15} D. {m � m � 15} 4.
5. ��23�s � 6
A. {s � s � �9} B. {s � s � 9} C. {s � s � 9} D. {s � s � �9} 5.
6. �1.1t � 4.62A. {t � t � 5.72} B. {t � t � 5.72} C. {t � t � �4.2} D. {t � t � �4.2} 6.
7. 5z � 4 � 2z � 8A. {z � z � 4} B. {z � z � 1} C. {z � z � 4} D. {z � z � 1} 7.
8. �2 �
24b� � 3b � 6
A. {b � b � �5} B. {b � b � �5} C. {b � b � �2} D. {b � b � �2} 8.
9. 7 � 9r � (r � 12) � 25
A. {r � r � �3} B. �r � r � ��35�� C. {r � r � �3} D. �r � r � ��
35�� 9.
10. The sum of two consecutive integers is at most 7. What is the largest possible value for the lesser integer?A. 1 B. 3 C. 2 D. 5 10.
11. Which of the following is the graph of the solution set of x � 0 or x � �4?A. B.
C. D. 11.�1�2�3�4�5�6 0 1 2�1�2�3�4�5�6 0 1 2
�1�2�3�4�5�6 0 1 2�1�2�3�4�5�6 0 1 2
66
© Glencoe/McGraw-Hill 384 Glencoe Algebra 1
Chapter 6 Test, Form 2B (continued)
12. Which compound inequality has the solution set shown in the graph?
A. �2 � y � 3 B. �2 � y � 3C. y � �2 or y � 3 D. �2 � y � 3 12.
13. Which of the following is the solution set of �3 � 2x � 7 � 13?A. {x � �5 � x � 3} B. {x � x � �5}C. {x � x � 3 or x � �5} D. {x � �5 � x � 3} 13.
14. Which of the following is the graph of the solution set of 7a � 3 � a � 15 or 5a � 3 � 8a?A. B.
C. D. 14.
15. Which of the following is the solution set of � 2x � 5 � 9?A. {�7, 2} B. {�7} C. {2} D. {�2, 7} 15.
16. The graph below represents the solution set of which inequality?
A. � 5x � 10 � � 10 B. � 5x � 10 � � 10C. � 5x � 10 � � 10 D. � 5x � 10 � � 10 16.
17. Which of the following is the solution set of � 4 � 7x � � 3?
A. �x � x � �17� or x � 1� B. {x � x is a real number}
C. �x � x � �17� or x � 1� D. {x � 1 � x � 7} 17.
18. Which ordered pair is part of the solution set of the inequality 5 � y � �3x?A. (2, �1) B. (�2, �1) C. (�3, �5) D. (3, �5) 18.
19. Which inequality is graphed?A. y � 2x � 1 B. y � �2x � 1C. y � 2x � 1 D. y � �2x � 1 19.
20. Alicia is planning to buy a new baseball glove and a new baseball bat with at most $196.Which inequality represents this situation if xrepresents the cost of a glove and y represents the cost of the bat she buys?A. y � 196 � x B. y � 196 � xC. 196 � y � x D. y � x � 196 20.
Bonus Solve 2 � 3x � 5(2 � x) � 3(2 � x) � 10. B:
�1�2 0 1 2 4 5 63
�1�2�3�4 0 1 2 43�1�2�3�4�5�6 0 1 2
�1�2�3�4�5�6 0 1 2�1�2�3�4�5�6 0 1 2
�1�2�3�4 0 1 2 43
NAME DATE PERIOD
66
y
xO
(�1, 1)
(0, �1)
Chapter 6 Test, Form 2C
© Glencoe/McGraw-Hill 385 Glencoe Algebra 1
Solve each inequality. Then graph your solution on a number line.
1. x � 12 � 1 1.
2. �14 � n � 5 2.
For Questions 3 and 4, solve each inequality.
3. 4 � �2 � t 3.
4. 7 � z � 3 4.
5. Define a variable, write an inequality, and solve: 5.The sum of 2 and a number is no greater than 7.
Solve each inequality.
6. �b8� � ��
15� 6.
7. �6t� � 14 7.
8. �19.8 � 3.6y 8.
9. �4r � 22 9.
10. �2a
5� 7� � 5 10.
11. 4x � 5 � 2x � 11 11.
12. 5( p � 2) � 2( p � 1) � 7p � 4 12.
13. 1.3(c � 4) � 2.6 � 0.7c 13.
For Questions 14–17, solve each compound inequality.Then graph the solution set.
14. 3w � 6 and �5 � w 14.
15. �4 � n or 3n � 1 � �2 15.
16. �1 � �3b
2� 4� � �
225� 16.
17. �4x � 8 � �4 or 7x � 5 � 16 17.
�1�2�3�4 0 1 2 43
�2 0 2 4 86
0
�1�2�3�4�5�6 0 1 2
�17�19�21 �15
131211109 14 15 1716
NAME DATE PERIOD
SCORE 66
Ass
essm
ent
© Glencoe/McGraw-Hill 386 Glencoe Algebra 1
Chapter 6 Test, Form 2C (continued)
18. Define a variable, write an inequality and solve. Felicita’s 18.bank charges $2.50 per month plus $0.10 per check. How many checks does she write if her bank charges are always between $3.50 and $5.00?
Solve each open sentence. Then graph the solution set.
19. � 1 � y � 2 19.
20. � 3 � 2x � � 1 20.
Solve each open sentence.
21. � 8x � 2 � 14 21.
22. � 3w � 1 � � 8 22.
For Questions 22 and 23, graph each inequality.
23. y � ��13�x � 2 23.
24. 2x � 3y � 12 24.
25. EXPENSES Camille has no more than $20.00 to spend each 25.week for lunch and bus fare. Lunch costs $3.00 each day, and bus fare is $0.75 each ride. Write an inequality for this situation. Can Camille buy lunch 5 times and ride the bus 8 times in one week?
Bonus Graph the solution set of the compound inequality B:3 � � x � 4 � � 7.
y
xO
y
xO
�1�2�3�4 0 1 2 43
�1�2�3�4 0 1 2 43
NAME DATE PERIOD
66
Chapter 6 Test, Form 2D
© Glencoe/McGraw-Hill 387 Glencoe Algebra 1
Solve each inequality. Then graph your solution on a number line.
1. y � 7 � 5 1.
2. m � 6 � �3 2.
For Questions 3 and 4, solve each inequality.
3. 3 � s � 6 3.
4. 8 � k � 13 4.
5. Define a variable, write an inequality, and solve: 5.14 is greater than a number plus 5.
Solve each inequality.
6. �h3� � 9 6.
7. ��23� � �5
z� 7.
8. 9.8 � 2.8k 8.
9. �3m � �18 9.
10. �3 �
24f
� � 1 10.
11. 5t � 8 � 3t � 3 11.
12. 3(�w � 6) � 2(2w � 8) � 1 12.
13. 1.9 � 1.7x � 2.1(3 � x) 13.
For Questions 14–17, solve each compound inequality.Then graph the solution set.
14. 7w � 14 and w � 3 14.
15. �w3� � 1 or 3w � 5 � 11 15.
16. 1 � �2y
4� 3� � �
141� 16.
17. 2 � 3x � 8 or 4 � 7x � �17 17.
�1�2�3�4 0 1 2 43
�1�2 0 1 2 4 5 63
0
�1�2�3�4 0 1 2 43
�7�9�11 �5
1312111098 14 15 16
NAME DATE PERIOD
SCORE 66
Ass
essm
ent
© Glencoe/McGraw-Hill 388 Glencoe Algebra 1
Chapter 6 Test, Form 2D (continued)
18. Define a variable, write an inequality and solve. Jose’s bank 18.charges $3.75 per month plus $0.10 per check. How many checks does he write if his bank charges are always between $5.75 and $7.25?
Solve each open sentence. Then graph the solution set.
19. � z � 4 � 7 19.
20. � w � 1 � � 4 20.
Solve each open sentence.
21. � 2x � 5 � 3 21.
22. � 4 � 3c � � 5 22.
For Questions 23 and 24, graph each inequality.
23. y � 3x 23.
24. 2y � 4x � 8 24.
25. SHOPPING Matthew is shopping for shoes and socks. He 25.has $75.00 to spend. The shoes he likes cost $28.00, and the socks cost $4.00. Write an inequality for this situation. Can Matthew buy 2 pairs of shoes and 5 pairs of socks?
Bonus Graph the solution set of the compound inequality B:� x � 1 � � 4 or � x � 1 � � 6.
y
xO
y
xO
�1�2�3 0 1 2 4 53
�11 30
NAME DATE PERIOD
66
Chapter 6 Test, Form 3
© Glencoe/McGraw-Hill 389 Glencoe Algebra 1
Solve each inequality. Then graph your solution on a number line.
1. m � (�3.4) � 12.7 1.
2. t � (�4) � 32 2.
Define a variable, write an inequality, and solve each problem.
3. Negative three sevenths plus a number is at least 2. 3.
4. A number less 15 is greater than the sum of twice the 4.number and 8.
Solve each inequality.
5. �2.6 � �w4� 5.
6. �11t � �9 6.
7. 2 � 3b � �11 �
715b� 7.
8. 5x � 3(x � 6) � 0 8.
9. �3x � 2(6x � 7) � 4(3 � 2x) � 17x � 8 9.
Define a variable, write an inequality, and solve each problem.
10. Raul plans to spend $78.00 on two shirts and a pair of 10.jeans. He bought the two shirts for $19.89 each. How much can he spend on the jeans?
11. The sum of two consecutive positive even integers is at 11.most 15. What are the possible pairs of integers?
12. Susan makes 10% commission on her sales. She also 12.receives a salary of $25,600. How much must she sell to receive a total income between $32,500 and $41,900?
NAME DATE PERIOD
SCORE 66
Ass
essm
ent
© Glencoe/McGraw-Hill 390 Glencoe Algebra 1
Chapter 6 Test, Form 3 (continued)
Solve each compound inequality, and graph the solution set.
13. 6 � 4m � 10 and 4(m � 2) � 6 � 3m 13.
14. ��n2� � 3 or 2n � 3 � 12 14.
15. 2(x � 14) � x � 7(x � 2) � x � x � 70 15.
For Questions 16–18, solve each open sentence. Then graph the solution set.
16. � 5x � 3 � � 17 16.
17. ��4x � 8 � � 16 17.
18. � �3 �
52x
� � 1 18.
19. Graph �y � 3x. 19.
20. DOGS Each afternoon Maria walks the dogs at a local pet 20.shelter for up to 2 hours. Maria spends 16 minutes walking a large dog and 12 minutes walking a small dog. Write an inequality for this situation. If Maria walked 9 dogs in one afternoon, what is the greatest number of large dogs that she could have walked that afternoon?
Bonus If xy � 0, determine if the compound inequality, B:2x � 1 � 7 and 4 � y � 3, is true or false.Explain your reasoning.
y
xO
NAME DATE PERIOD
66
Chapter 6 Open-Ended Assessment
© Glencoe/McGraw-Hill 391 Glencoe Algebra 1
Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.
1. Solve 10n � 7(n � 2) � 5n � 12. Explain each step in yoursolution.
2. Draw a line on a coordinate plane so that you can determine atleast two points on the graph.a. Write an inequality to represent one of the half planes created
by the line.b. Determine if the solution set of the inequality written for part
a includes the line or not. Explain your response.
3. Let b � 2. Describe how you would determine if ab � 2a.
4. a. Explain why the solution set for � x � � 3 is {�3, 3}.b. Determine if the open sentence � x � 2 � � 4 and the compound
inequality �2x � 4 or x � 6 have the same solution set.
5. ARCHITECTURE An architect is designing a house for theFrazier family. In the design, she must consider the desires of thefamily and the local building codes. The rectangular lot on whichthe house will be built is 158 feet long, and 90 feet wide.a. The building codes state that one can build no closer than
20 feet to the lot line. Write an inequality to represent thepossible widths of the house along the 90-foot dimension. Solvethe inequality.
b. The Fraziers requested that the rectangular house contain noless than 2800 square feet and no more than 3200 square feetof floor space. If the house has only one floor, use themaximum value for the width of the house from part a, andexplain how to use an inequality to find the possible lengths.
c. The Fraziers have asked that the cost of the house be about$175,000 and are willing to deviate from this price no morethan $20,000. Write an open sentence involving an absolutevalue and solve. Explain the meaning of the answer.
NAME DATE PERIOD
SCORE 66
Ass
essm
ent
© Glencoe/McGraw-Hill 392 Glencoe Algebra 1
Chapter 6 Vocabulary Test/Review
Write whether each sentence is true or false. If false, replace the underlined word or number to make a true sentence.
1. The Addition Property of Inequalities states that if the 1.same number is added to each side of a true inequality,the resulting inequality is true.
2. An inequality defines the boundary or edge for each 2.half-plane.
3. A compound inequality containing and is true if one or both 3.of the inequalities is true.
4. According to the Division Property of Inequalities, if each 4.side of a true inequality is divided by the same positivenumber, the direction of the inequality symbol must be reversed so that the resulting inequality is also true.
5. The solution set for an inequality that contains two 5.variables consists of many ordered pairs which fill a region on the coordinate plane called a half-plane.
6. The graph of a compound inequality containing and is the 6.intersection of the graphs of the two inequalities.
7. The Division Property of Inequalities states that if each 7.side of a true inequality is divided by the same negativenumber, the resulting inequality is also true.
8. Set-builder notation is a way of writing a solution set. 8.
9. If the same number is subtracted from each side of a true 9.inequality, the resulting inequality is also true.
10. The graph of a compound inequality containing and is the 10.union of the graphs of the two inequalities.
In your own words—
11. Explain how to use the Multiplication Property of Inequalities
to solve the inequality ��23�x � 7.
Addition Property of Inequalities
boundarycompound inequality
Division Property of Inequalities
half-planeintersection
Multiplication Property of Inequalities
set-builder notation
Subtraction Property of Inequalities
union
NAME DATE PERIOD
SCORE 66
Chapter 6 Quiz (Lessons 6–1 and 6–2)
66
© Glencoe/McGraw-Hill 393 Glencoe Algebra 1
Solve each inequality. Then graph your solution on a number line.
1. n � 11 � 3 1.
2. w � 9 � �5 2.
For Questions 3 and 4, solve each inequality. 3.
3. � 4 � �4 � r 4. �14� � m �
34� 4.
5. Define a variable, write an inequality, and solve: 5.A number decreased by 7 is at least 15.
Solve each inequality.6. �1
m3�
� �6 7. ��49� � ��1
52�
r 6.
7.
8. �3n � 84 9. �3.22 1.4w 8.
9.10. STANDARDIZED TEST PRACTICE Which inequality does not
have the solution {x � x � �2}?
A. �3x � 6 B. ��2x
� � 1
C. 7x � �14 D. �43�x � ��
83� 10.
13121110 14 15 17 1816
13121110 14 15 17 1816
NAME DATE PERIOD
SCORE
Chapter 6 Quiz (Lesson 6–3)
For Questions 1–8, solve each inequality.
1. ��d5� � 12 8 1.
2. 9y � 6 � 2y � 15 2.
3. 3(y � 2) � 4(3 � 2y) � 6(3y � 1) � 11y 3.
4. 23 � t � 2(t � 9) � 3(t � 2) 4.
5. Define a variable, write an inequality, and solve. The sum 5.of a number and three is less than nineteen less the number.
NAME DATE PERIOD
SCORE 66
Ass
essm
ent
© Glencoe/McGraw-Hill 394 Glencoe Algebra 1
1. Solve �14 � 3x � 1 � 1. Then graph the solution set. 1.
2. Solve the compound inequality 2y � 3 � 7 or �3y � �18. 2.Then graph the solution set.
3. Define a variable, write an inequality and solve. 3.Eight times a number is between 16 and 40.
4. Solve � 2x � 5 � � 3. 4.
5. Write an open sentence involving absolute value for this 5.graph.
�1�2�3�4 0 1 2 43
0 1 2 4 5 6 7 83
�1�2�3�4�5�6 0 1 2
Chapter 6 Quiz (Lesson 6–6)
1. From the set {(0, 1), (3, �3), (4, 2), (�1, 2)}, which ordered 1.pairs are part of the solution set for x � y � 0?
For Questions 2 and 3, graph each inequality.
2. x � 3 2.
3. �2(x � y) � 4 3.
4. CLOTHING Rita plans to spend at most $230.00 on a new 4.wardrobe. The skirts she wants to buy cost $35 each, and the blouses cost $25 each. Write an inequality that represents the number of skirts and blouses Rita can buy. Can Rita buy 4 skirts and 4 blouses?
y
xO
NAME DATE PERIOD
SCORE
Chapter 6 Quiz (Lessons 6–4 and 6–5)
66
NAME DATE PERIOD
SCORE
66
y
xO
Chapter 6 Mid-Chapter Test (Lessons 6–1 through 6–3)
© Glencoe/McGraw-Hill 395 Glencoe Algebra 1
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1–3, solve each inequality.
1. r � �78� � 1
A. �r � r � �18�� B. �r � r � �
18�� C. �r � r � 1�
78�� D. �r � r � 1�
78�� 1.
2. 12x � 5 17x � 10A. {x � x � �3} B. {x � x 3} C. {x � x �3} D. {x � x � 3} 2.
3. 6m � 2(7 � 3m) � 5(2m � 3) � m
A. {m � m � 1} B. �m � m � �19�� C. {m � m � 1} D. �m � m � �
19�� 3.
4. Four less than three times a number is at most five.Which of the following describes the number?A. any number less than 3B. any number greater or equal to 3C. any number less than or equal to 3
D. any number less than or equal to �13� 4.
Solve and check each inequality.
5. 4.2 � �11 � t 5.
6. ��35�v � ��1
45�
6.
Define a variable, write an inequality, and solve each problem.
7. For a package to qualify for a certain postage rate, the 7.sum of its length and girth cannot exceed 85 inches.If the girth is 63 inches, how long can the package be?
8. The minimum daily requirement of vitamin C for 8.14-year-olds is at least 50 mg per day. An average-sized apple contains 6 mg of vitamin C. How many apples would a person have to eat each day to satisfy this requirement?
Part II
Part I
NAME DATE PERIOD
SCORE 66
Ass
essm
ent
© Glencoe/McGraw-Hill 396 Glencoe Algebra 1
Chapter 6 Cumulative Review (Chapters 1–6)
NAME DATE PERIOD
66
1. Simplify 4(2y � 5) � 6(4y � 3). (Lesson 1–6) 1.
2. Name the set or sets of numbers to which the real number 2.0 belongs. (Lesson 2–7)
3. Solve 3x � �23�. (Lesson 3–3) 3.
4. State whether the percent of change is a percent of increase 4.or a percent of decrease. Then find the percent of change.(Lesson 3–7)
original: 76new: 57
5. Express the relation {(�2, 1), (3, �1), (2,�2), (�2, 0)} as a 5.mapping. Then write the inverse of the relation. (Lesson 4–3)
6. Determine whether the sequence �6, �3, 0, 3 … is an 6.arithmetic sequence. If it is, state the common difference.(Lesson 4–7)
7. Find the slope of the line that passes through (�2, 0) and 7.(5, �8). (Lesson 5–1)
8. The Lopez family drove 165 miles in 3 hours. Write a direct 8.variation equation for the distance driven in any time. How far can the Lopez family drive in 5 hours? (Lesson 5–2)
9. Write an equation of a line that passes through (�2, �1) 9.with slope 3. (Lesson 5–4)
10. Draw a scatter plot of the relation, and determine what 10.relationship exists, if any, in the data. (Lesson 5–7)
{(1, 5), (1, 8), (2, 7), (3, 5), (3, 8), (4, 4), (5, 3), (5, 5),(6, 2), (7, 4), (8, 1), (9, 2)}
11. Solve 12 � r � 15. Then graph the solution. (Lesson 6–1) 11.
12. Solve �2u �7
15� 3. (Lesson 6–3) 12.
13. Define a variable, write a compound inequality, and solve 13.the problem. (Lesson 6–4)
Seven less than twice a number is greater than 13 or less than or equal to �5.
14. Solve �3x � 4� � 5. Then graph the solution set. (Lesson 6–5) 14.
�1�2�3�4 0 1 2 43
�1�2�3�4 0 1 2 43
y
xO 1
123456789
2 3 4 5 6 7 8 9
X Y
Standardized Test Practice (Chapters 1–6)
© Glencoe/McGraw-Hill 397 Glencoe Algebra 1
NAME DATE PERIOD
66
Ass
essm
ent
1. Evaluate [1 � 4(5)] � [3(9) � 7]. (Lesson 1–2)
A. 45 B. 27 C. 41 D. 31 1.
2. If a person’s birthday is in January, what are the odds that it is between the 20th and the 29th, inclusively? (Lesson 2–6)
E. �1301�
F. �281�
G. �2311�
H. �1201�
2.
3. How many liters of a 10% saline solution must be added to 4 liters of a 40% saline solution to obtain a 15% saline solution? (Lesson 3–9)
A. 20 L B. 4 L C. 2 L D. 48 L 3.
4. The currency exchange rate between the U.S. and Canada in 1999 could be modeled by the equation d � 1.49c where d represents the number of U.S. dollars and c represents the number of Canadian dollars. Solve the equation for Canadian dollar amounts of $1, $2,$5, and $20. (Lesson 4–4)
E. {(1, 1.49), (2, 2.98), (5, 7.45), (20, 29.8)F. {(1, 1.5), (2, 3), (5, 7.5), (20, 30)}G. {(1, 0.67), (2, 1.34), (5, 3.36), (20, 13.42)}H. {(1, 2.49), (2, 3.49), (5, 6.49), (20, 21.49)} 4.
5. If a line passes through (0, �6) and has a slope of �3, what is the equation of the line? (Lesson 5–3)
A. y � �6x � 3 B. x � �6y � 3 C. y � �3x � 6 D. x � �3y � 6 5.
6. If r is the slope of a line, and s is the slope of a line perpendicular to that line, what is the relationship between r and s? (Lesson 5–6)
E. There is no relationship. F. r � s
G. r � �s H. r � ��1s� 6.
7. Which inequality does not have the solution {t � t � 4}? (Lesson 6–2)
A. �t � �4 B. 3t � 12 C. �2t� � 2 D. ��8
t� � ��
12� 7.
8. Solve 4 � 2r 3(5 � r) � 7(r � 1). (Lesson 6–3)
E. �r � r � ��32�� F. {r � r � �3} G. {r � r � �2} H. �r � r � ��
94�� 8.
9. Write a compound inequality for the graph. (Lesson 6–4)
A. x � �1 and x 2 B. x � �1 or x 2C. x � �1 or x � 2 D. x � �1 and x � 2 9. DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
Part I: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
�1�2�3�4 0 1 2 43
© Glencoe/McGraw-Hill 398 Glencoe Algebra 1
Standardized Test Practice (continued)
NAME DATE PERIOD
66
NAME DATE PERIOD
10. Find the 13th term of the arithmetic sequence 10. 11.
�12�, �
34�, 1, 1�
14�, 1�
12�, ... . (Lesson 4–7)
11. If y � 18 when x � 16, find y when x � 6.(Lesson 5–2)
For Questions 12 and 13, determine the value that is missing.
12. The solution set is {n � n 15} for the 12. 13.inequality n � 7 ___. (Lesson 6–1)
13. If � a � 8 � � 17, then a � ___ or a � �9.(Lesson 6–5)
Column A Column B
14. 14.
(Lesson 3–7)
15. 15.
(Lesson 5–6)
16. �3 � 2x � 1 � 7 16.
(Lesson 6–4)
�2x
�4x
DCBA
DCBAThe slope of any line
perpendicular to y � 4x � 3.The slope of the line
y � 4x � 3.
DCBAthe percent of change if
original: 40 new: 50the percent of change if
original: 35 new: 49
Part 3: Quantitative Comparison
Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
A
D
C
B
Part 2: Grid In
Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
First Semester Test (Chapters 1–6)
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 399 Glencoe Algebra 1
For Questions 1–20, write the letter for the correct answer in the blank at the right of each question.
1. Evaluate 4v2 � (n2 � 3s) if n � 8, s � 4, and v � 7.A. 120 B. 732 C. 32 D. 144 1.
2. Simplify 9a2 � 7a � 4a2 � 2a.A. 13a2 � 9a B. 22a3 C. 36a2 � 14a D. 16a2 � 6a 2.
3. Identify the conclusion of the statement.If the oven works properly, then we will learn how to cook.A. The oven works properly. B. The oven is new.C. I already know how to cook. D. We will learn how to cook. 3.
4. Evaluate � x � 2 � � �34� if x � �
151�.
A. �9290�
B. �5210�
C. �1290�
D. ��2101� 4.
5. The land areas in square miles of the 19 zip codes in Guam are listed below.Use a stem-and-leaf plot to determine which measure of central tendency is equal to 7.1 1 10 6 9 6 30 6 6 19 10 6 2 7 17 1 17 35 20A. mean B. median C. mode D. frequency 5.
6. Name the set of numbers to which the real number �196� does not belong.A. rational number B. integerC. irrational number D. natural number 6.
7. Translate the sentence into an equation. Twelve times a number r is the same as two times the sum of r and p.A. 12r � 2(r � p) B. 12r � 2r � pC. 12 � r � 2(r � p) D. 12 � r � 2r � p 7.
8. Solve �56�h � �30.
A. �25 B. �180 C. �150 D. �36 8.
9. Solve 5(a � 12) � 8(3a � 2).
A. ��1149�
B. �4 C. 3 D. ��4249�
9.
10. The surface area A of a sphere is A � 4�r2 where r is the radius of the sphere. What is the radius, rounded to the nearest tenth, of a ball with surface area equal to 85 square inches?A. 2.6 in. B. 6.8 in. C. 2.7 in. D. 6.7 in. 10.
Ass
essm
ent
© Glencoe/McGraw-Hill 400 Glencoe Algebra 1
First Semester Test (continued)(Chapters 1–6)
11. The coordinates of the vertices of rectangle MNOP are M(�2, 1), N(4, 3),O(5, 0), and P(�1, �2). If the rectangle is reflected over the x-axis, which point below has the correct coordinates?A. M(2, 1) B. N(4, �3) C. O(�5, 0) D. P(�2, �1) 11.
12. The graph of the line is the graph of which equation?A. 3x � 2y � 12 B. 3x � 2y � 12C. 3x � 2y � �12 D. 3x � 2y � �12 12.
13. If f(x) � 4x � 5, find f(3a � 1).A. 12a � 4 B. 7a � 4C. 12a � 1 D. 12a � 4x � 5 13.
14. The average rate of change for the combined population of San Diego,California and Tijuana, Mexico was 0.0825 million people per year from 1990 to 2000. If the 2000 population was about 4 million, what was the approximate 1990 population? Source: Time Magazine
A. 4.25 million B. 3.9 million C. 3.175 million D. 1.4 million 14.
15. A line passes through (�1, 3) and (1, �3). Which equation does notrepresent the line?A. (y � 3) � �3(x � 1) B. 3x � y � 0C. (y � 3) � �3(x � 1) D. y � �3x 15.
16. Write the slope-intercept form of an equation for the line that passes through (4, 0) and is parallel to the graph of 3y � 6x � 4.A. y � 2x � 8 B. 2y � �x C. y � 2x � 4 D. y � �2x � 8 16.
17. Solve 8r � 14 � 12r � 6.A. {r � r � �2} B. {r � r � 2} C. {r � r � 2} D. {r � r � �2} 17.
18. Solve 8 � 2h � 6 � 22.A. {h� 4 � h � 11} B. {h� 7 � h � 14}C. {h� 1 � h � 8} D. {h� 0 � h � 14} 18.
19. Which graph represents the solution of � n � 5 � � 1?A. B.
C. D. 19.
20. Which ordered pair is not a solution of 4x � 8y 24?A. (2, �2) B. (�5, �4) C. (7, �1) D. (�8, �8) 20.
�4�3�2�1 0 2 3 4 5 6 71�1 0 1 2 3 4 5 6 7 8 9 10
�9�8�7�6�5�4�3�2�1 0 21�1�2�3�5�6 �4 0 1 2 3 4 5
NAME DATE PERIOD
y
xO
First Semester Test (continued)(Chapters 1–6)
© Glencoe/McGraw-Hill 401 Glencoe Algebra 1
21. Evaluate �3abc� c2� if a � 14, b � 3, and c � 7. 21.
22. Find the solution set for 18 � 3x 9 if the replacement set 22.is {1, 2, 3, 4, 5, 6}.
23. Name the property used in the equation n � 5 � 0. Then 23.find the value of n.
24. Simplify 4.1(x � 2y) � 2.7(x � y) � 5x. 24.
25. Find a counterexample for the statement. If you visit an 25.art gallery, then you will see a painting by Monet.
26. Name the coordinates of the 26.points graphed on the number line.
27. Simplify 4x( � 7y) � (5u)(3v) � 11uv. 27.
28. Evaluate �uv �w
12� if u � 3.6, v � 4, and w � 6. 28.
29. A card is selected at random from a standard deck of 29.52 cards. What are the odds against selecting a heart?
30. Solve the following problem by working backward. A father 30.made a batch of cookies. His son ate four and gave six to a friend. Two of his daughters ate half of the remaining cookies. The father was left with thirteen cookies. How many cookies did the father make?
For Questions 31 and 32, solve each equation. 31.
31. �m6� � �
168� 32. 2(3y � 2) � y 32.
33. State whether the percent of change is a percent of increase 33.or a percent of decrease. Then find the percent of change.original: 180new: 207
34. Two airplanes leave Phoenix at the same time and fly in 34.opposite directions. One plane travels 60 miles per hour
faster than the other. After 2�12� hours they are 1700 miles
apart. What is the rate of the slower plane?
35. Identify the transformation as a reflection, 35.translation, dilation, or rotation.
NAME DATE PERIOD
�4�5 �3�2�1 0 2 3 4 5 61
Ass
essm
ent
© Glencoe/McGraw-Hill 402 Glencoe Algebra 1
First Semester Test (continued)(Chapters 1–6)
36. Express the relation shown in the 36.graph as a set of ordered pairs. Then write the inverse of the relation.
37. Graph y � 2x � 3. 37.
38. Write an equation for the nth term of the arithmetic 38.sequence 7, 11, 15, 19, … .
39. Ms. Ortiz paid $38 for 20 gallons of gasoline. Write a direct 39.variation equation relating the cost of gasoline C to the number of gallons purchased n.
40. Find the slope, y-intercept, and x-intercept of the line 40.represented by the equation 3x � 4y � 8.
41. Find the value of r so that the line through (2, 3) and (r, �3) 41.
has a slope perpendicular to the graph of y � ��16�x � 3.
For Questions 42 and 43, use the table that shows UV indices and humidities for 6 cities on a July day.
42. Use a scatter plot to determine what relationship, if any, 42.exists in the data.
43. Write the slope-intercept form of an equation for a line of 43.fit.
For Questions 44 and 45, solve each inequality. 44.
44. �5t
2� 9� � 4t 45. 2(5x � 4) 7(x � 2) 45.
46. Solve 4x � 9 � 1 or 3x 15. Then graph the solution set. 46.
47. Solve � 2u � 7 � � 13. 47.
�4�3�2�1 0 2 3 4 5 6 71
y
xO
NAME DATE PERIOD
y
xO
UV Index 4 4 6 7 8 10
Humidity Forecast (Percent) 74 80 63 52 55 29
Standardized Test PracticeStudent Record Sheet (Use with pages 364–365 of the Student Edition.)
© Glencoe/McGraw-Hill A1 Glencoe Algebra 1
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7
2 5 8
3 6 9
Solve the problem and write your answer in the blank.
For Questions 11 and 15, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.
10 11 15
11 (grid in)
12
13
14
15 (grid in)
16
17
18
Record your answers for Questions 19–21 on the back of this paper.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
DCBADCBADCBA
DCBADCBADCBA
DCBADCBADCBA
NAME DATE PERIOD
66
An
swer
s
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 3 Extended ResponsePart 3 Extended Response
Part 1 Multiple ChoicePart 1 Multiple Choice
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g In
equ
alit
ies
by A
ddit
ion
an
d S
ub
trac
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-1
6-1
©G
lenc
oe/M
cGra
w-H
ill34
3G
lenc
oe A
lgeb
ra 1
Lesson 6-1
Solv
e In
equ
alit
ies
by
Ad
dit
ion
Add
itio
n c
an b
e u
sed
to s
olve
in
equ
alit
ies.
If a
ny
nu
mbe
r is
add
ed t
o ea
ch s
ide
of a
tru
e in
equ
alit
y,th
e re
sult
ing
ineq
ual
ity
is a
lso
tru
e.
Ad
dit
ion
Pro
per
ty o
f In
equ
alit
ies
For
all
num
bers
a,
b, a
nd c
, if
a�
b, t
hen
a�
c�
b�
c,
and
if a
�b,
the
n a
�c
�b
�c.
Th
e pr
oper
ty i
s al
so t
rue
wh
en �
and
�ar
e re
plac
ed w
ith
�an
d �
.
Sol
ve x
�8
��
6.T
hen
gra
ph
it
on a
nu
mb
er l
ine.
x�
8 �
�6
Orig
inal
ineq
ualit
y
x�
8 �
8 �
�6
�8
Add
8 t
o ea
ch s
ide.
x�
2S
impl
ify.
Th
e so
luti
on i
n s
et-b
uil
der
not
atio
n i
s {x
|x�
2}.
Nu
mbe
r li
ne
grap
h:
�4
�3
�2
�1
01
23
4
Sol
ve 4
�2a
��
a.T
hen
grap
h i
t on
a n
um
ber
lin
e.
4 �
2a�
�a
Orig
inal
ineq
ualit
y
4 �
2a�
2a�
�a
�2a
Add
2a
to e
ach
side
.
4 �
aS
impl
ify.
a�
44
�a
is t
he s
ame
as a
�4.
The
sol
utio
n in
set
-bui
lder
not
atio
n is
{a|
a�
4}.
Nu
mbe
r li
ne
grap
h:
�2
�1
01
23
45
6
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on,a
nd
gra
ph
it
on a
nu
mb
er l
ine.
1.t
�12
�16
{tt
�28
}2.
n�
12 �
6{n
n�
18}
3.6
�g
�3
{gg
�9}
4.n
�8
��
13{n
n�
�5}
5.�
12 �
�12
�y
{yy
�0}
6.�
6 �
s�
8{s
s�
2}
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on.
7.�
3x�
8 �
4x8.
0.6n
�12
�0.
4n9.
�8k
�12
��
9k{x
x�
8}{n
n�
12}
{kk
�12
}
10.�
y�
10 �
15 �
2y11
.z�
�12
.�2b
��
4 �
3b
{yy
�25
}�z
z�
1�
{bb
��
4}
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.13
–15.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
13.A
nu
mbe
r de
crea
sed
by 4
is
less
th
an 1
4.n
�4
�14
;{n
n�
18}
14.T
he
diff
eren
ce o
f tw
o n
um
bers
is
mor
e th
an 1
2,an
d on
e of
th
e n
um
bers
is
3.n
�3
�12
;{n
n�
15}
15.F
orty
is
no
grea
ter
than
th
e di
ffer
ence
of
a n
um
ber
and
2.40
�n
�2;
{nn
�42
}
2 � 34 � 31 � 3
�4
�2
�1
01
23
�3
4�
3�
4�
2�
10
12
34
�9
�10
�8
�7
�6
�5
�4
�3
�2
78
910
1112
1314
1514
1512
1316
1718
1920
2627
2829
3031
3233
34
©G
lenc
oe/M
cGra
w-H
ill34
4G
lenc
oe A
lgeb
ra 1
Solv
e In
equ
alit
ies
by
Sub
trac
tio
nS
ubtr
acti
on c
an b
e us
ed t
o so
lve
ineq
ualit
ies.
If a
nynu
mbe
r is
sub
trac
ted
from
eac
h si
de o
f a
true
ine
qual
ity,
the
resu
ltin
g in
equa
lity
is
also
tru
e.
Su
btr
acti
on
Pro
per
ty o
f In
equ
alit
ies
For
all
num
bers
a,
b, a
nd c
, if
a�
b, t
hen
a�
c�
b�
c,
and
if a
�b,
the
n a
�c
�b
�c.
Th
e pr
oper
ty i
s al
so t
rue
wh
en �
and
�ar
e re
plac
ed w
ith
�an
d �
.
Sol
ve 3
a�
5 �
4 �
2a.T
hen
gra
ph
it
on a
nu
mb
er l
ine.
3a�
5 �
4 �
2aO
rigin
al in
equa
lity
3a�
5 �
2a�
4 �
2a�
2aS
ubtr
act
2afr
om e
ach
side
.
a�
5 �
4S
impl
ify.
a�
5 �
5 �
4 �
5S
ubtr
act
5 fr
om e
ach
side
.
a�
�1
Sim
plify
.
Th
e so
luti
on i
s {a
a�
�1}
.N
um
ber
lin
e gr
aph
:
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on,a
nd
gra
ph
it
on a
nu
mb
er l
ine.
1.t
�12
�8
2.n
�12
��
123.
16 �
h�
9{t
t�
�4}
{nn
��
24}
{hh
�7}
4.y
�4
��
25.
3r�
6 �
4r6.
q�
5 �
q
{yy
��
6}{r
r�
6}{q
q�
5}
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on.
7.4p
�3p
�0.
78.
r�
�9.
9k�
12 �
8k
{pp
�0.
7}�r
r�
�{k
k�
�12
}
10.�
1.2
�2.
4 �
y11
.4y
�5y
�14
12.3
n�
17 �
4n{y
y�
�3.
6}{y
y�
�14
}{n
n�
17}
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.13
–15.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
13.T
he
sum
of
a n
um
ber
and
8 is
les
s th
an 1
2.n
�8
�12
;{n
n�
4}
14.T
he
sum
of
two
nu
mbe
rs i
s at
mos
t 6,
and
one
of t
he
nu
mbe
r is
�2.
n�
(�2)
�6;
{nn
�8}
15.T
he s
um o
f a
num
ber
and
6 is
gre
ater
tha
n or
equ
al t
o �
4.n
�6
��
4;{n
n�
�10
}
1 � 83 � 81 � 4
21
03
45
67
82
34
56
79
18
�8
�7
�6
�5
�4
�3
�2
�1
0
1 � 23 � 2
56
78
910
1112
13�
26�
25�
24�
23�
22�
21�
6�
5�
4�
3�
2�
10
12
�4
�3
�2
�1
01
23
4
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g In
equ
alit
ies
by A
ddit
ion
an
d S
ub
trac
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-1
6-1
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 6-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
So
lvin
g In
equ
alit
ies
by A
ddit
ion
an
d S
ub
trac
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-1
6-1
©G
lenc
oe/M
cGra
w-H
ill34
5G
lenc
oe A
lgeb
ra 1
Lesson 6-1
Mat
ch e
ach
in
equ
alit
y w
ith
its
cor
resp
ond
ing
grap
h.
1.x
�11
�16
ca.
2.x
�6
�1
eb
.
3.x
�2
��
3a
c.
4.x
�3
�1
bd
.
5.x
�1
��
7d
e.
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on,a
nd
gra
ph
it
on a
nu
mb
er l
ine.
6.d
�5
�1
{dd
�6}
7.s
�9
�8
{ss
��
1}
8.a
�7
��
13{a
a�
�6}
9.w
�1
�4
{ww
�5}
10.4
�k
�3
{kk
�1}
11.�
9 �
b�
4{b
b�
�5}
12.�
2 �
x�
4{x
x�
�6}
13.2
y�
y�
2{y
y�
2}
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.14
–18.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
14.A
nu
mbe
r de
crea
sed
by 1
0 is
gre
ater
th
an �
5.n
�10
��
5;{n
n�
5}
15.A
nu
mbe
r in
crea
sed
by 1
is
less
th
an 9
.n
�1
�9;
{nn
�8}
16.S
even
mor
e th
an a
num
ber
is l
ess
than
or
equa
l to
�18
.n
�7
��
18;{
n n
��
25}
17.T
wen
ty l
ess
than
a n
um
ber
is a
t le
ast
15.
n�
20 �
15;
{nn
�35
}
18.A
nu
mbe
r pl
us
2 is
at
mos
t 1.
n�
2 �
1;{n
n�
�1}
�2
�1
�4
�3
01
23
4�
6�
5�
8�
7�
4�
3�
2�
10
�8
�7
�6
�5
�4
�3
�2
�1
0�
2�
1�
4�
30
12
34
23
01
45
67
8�
8�
7�
6�
5�
4�
3�
2�
10
�2
�1
�4
�3
01
23
42
30
14
56
78
01
23
45
67
8
�8
�7
�6
�5
�4
�3
�2
�1
087
65
43
21
0
43
21
0�
1�
2�
3�
4
�8
�7
�6
�5
�4
�3
�2
�1
0
©G
lenc
oe/M
cGra
w-H
ill34
6G
lenc
oe A
lgeb
ra 1
Mat
ch e
ach
in
equ
alit
y w
ith
its
cor
resp
ond
ing
grap
h.
1.�
8 �
x�
15b
a.
2.4x
�3
�5x
db
.
3.8x
�7x
�4
ac.
4.12
�x
�9
cd
.
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on,a
nd
gra
ph
it
on a
nu
mb
er l
ine.
5.r
�(�
5) �
�2
{rr
��
7}6.
3x�
8 �
4x{x
x�
8}
7.n
�2.
5 �
�5
{nn
��
2.5}
8.1.
5 �
y�
1{y
y�
0.5}
9.z
�3
��z
z�
�2
�10
.�
c�
�c c
�1
�
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.11
–14.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
11.T
he
sum
of
a n
um
ber
and
17 i
s n
o le
ss t
han
26.
n�
17 �
26;
{nn
�9}
12.T
wic
e a
nu
mbe
r m
inu
s 4
is l
ess
than
th
ree
tim
es t
he
nu
mbe
r.2n
�4
�3n
;{n
n�
�4}
13.T
wel
ve i
s at
mos
t a
nu
mbe
r de
crea
sed
by 7
.12
�n
�7;
{nn
�19
}
14.E
igh
t pl
us
fou
r ti
mes
a n
um
ber
is g
reat
er t
han
fiv
e ti
mes
th
e n
um
ber.
8 �
4n�
5n;
{nn
�8}
15.A
TMO
SPH
ERIC
SC
IEN
CE
Th
e tr
opos
pher
e ex
ten
ds f
rom
th
e ea
rth
’s s
urf
ace
to a
hei
ght
of 6
–12
mil
es,d
epen
din
g on
th
e lo
cati
on a
nd
the
seas
on.I
f a
plan
e is
fly
ing
at a
nal
titu
de o
f 5.
8 m
iles
,an
d th
e tr
opos
pher
e is
8.6
mil
es d
eep
in t
hat
are
a,h
ow m
uch
hig
her
can
th
e pl
ane
go w
ith
out
leav
ing
the
trop
osph
ere?
no
mo
re t
han
2.8
mi
16.E
AR
TH S
CIE
NC
EM
atu
re s
oil
is c
ompo
sed
of t
hre
e la
yers
,th
e u
pper
mos
t be
ing
tops
oil.
Jam
al i
s pl
anti
ng
a bu
sh t
hat
nee
ds a
hol
e 18
cen
tim
eter
s de
ep f
or t
he
root
s.T
he
inst
ruct
ion
s su
gges
t an
add
itio
nal
8 c
enti
met
ers
dept
h f
or a
cu
shio
n.I
f Ja
mal
wan
ts t
oad
d ev
en m
ore
cush
ion
,an
d th
e to
psoi
l in
his
yar
d is
30
cen
tim
eter
s de
ep,h
ow m
uch
mor
e cu
shio
n c
an h
e ad
d an
d st
ill
rem
ain
in
th
e to
psoi
l la
yer?
no
mo
re t
han
4 c
m
�4
�3
�2
�1
01
23
4�
4�
3�
2�
10
12
34
1 � 43 � 4
1 � 21 � 3
2 � 3
�4
�3
�2
�1
01
23
4�
4�
3�
2�
10
12
34
45
23
67
89
10�
8�
7�
6�
5�
4�
3�
2�
10
23
45
67
81
0�8
�7
�6
�5
�4
�3
�2
�1
087
65
43
21
0
21
0�
1�
2�
3�
4�
5�
6
Pra
ctic
e (
Ave
rag
e)
So
lvin
g In
equ
alit
ies
by A
ddit
ion
an
d S
ub
trac
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-1
6-1
Answers (Lesson 6-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
olv
ing
Ineq
ual
itie
s by
Add
itio
n a
nd
Su
btr
acti
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-1
6-1
©G
lenc
oe/M
cGra
w-H
ill34
7G
lenc
oe A
lgeb
ra 1
Lesson 6-1
Pre-
Act
ivit
yH
ow a
re i
neq
ual
itie
s u
sed
to
des
crib
e sc
hoo
l sp
orts
?
Rea
d th
e in
trod
uct
ion
to
Les
son
6-1
at
the
top
of p
age
318
in y
our
text
book
.
•U
se t
he
info
rmat
ion
in
th
e gr
aph
to
wri
te a
n i
neq
ual
ity
stat
emen
t ab
out
part
icip
atio
n i
n t
wo
spor
ts.
Sam
ple
an
swer
:F
or
soft
bal
l an
d t
rack
an
d f
ield
,13,
009
�14
,587
•R
ewri
te y
our
ineq
ual
ity
stat
emen
t to
sh
ow t
hat
40
sch
ools
add
ed b
oth
of
the
spor
ts.I
s th
e st
atem
ent
stil
l tr
ue?
Sam
ple
an
swer
:13
,049
�14
,627
;ye
s
Rea
din
g t
he
Less
on
Wri
te t
he
lett
er o
f th
e gr
aph
th
at m
atch
es e
ach
in
equ
alit
y.
1.x
��
1a.
2.x
��
1b
.
3.x
��
1c.
4.x
��
1d
.
5.U
se t
he
char
t to
wri
te a
sen
ten
ce t
hat
cou
ld b
e de
scri
bed
by t
he
ineq
ual
ity
3n�
2n�
7.T
hen
sol
ve t
he
ineq
ual
ity.
Ineq
ual
itie
s
��
��
less
tha
ngr
eate
r th
anat
mos
tat
leas
tfe
wer
tha
nm
ore
than
no m
ore
than
no le
ss t
han
less
tha
n or
equ
al t
ogr
eate
r th
an o
r eq
ual t
o
Sam
ple
an
swer
:Th
ree
tim
es a
nu
mb
er is
at
leas
t tw
o t
imes
th
e n
um
ber
plu
s 7;
n�
7
Hel
pin
g Y
ou
Rem
emb
er
6.T
each
ing
som
eon
e el
se c
an h
elp
you
rem
embe
r so
met
hin
g.E
xpla
in h
ow y
ou w
ould
tea
chan
oth
er s
tude
nt
wh
o m
isse
d cl
ass
to s
olve
th
e in
equ
alit
y 2x
�4
�3x
.
Su
btr
act
2xfr
om
eac
h s
ide.
Sim
plif
y.
32
10
�1
�2
�3
c3
21
0�
1�
2�
3a
�3
�2
�1
01
23
d�
3�
2�
10
12
3b
©G
lenc
oe/M
cGra
w-H
ill34
8G
lenc
oe A
lgeb
ra 1
Tria
ng
le In
equ
alit
ies
Rec
all
that
a l
ine
segm
ent
can
be
nam
ed b
y th
e le
tter
s of
its
en
dpoi
nts
.Lin
e se
gmen
t A
B(w
ritt
en a
s A �
B�)
has
poi
nts
Aan
d B
for
endp
oin
ts.T
he
len
gth
of A
Bis
wri
tten
wit
hou
t th
e ba
r as
AB
.
AB
�B
Cm
�A
�m
�B
Th
e st
atem
ent
on t
he
left
abo
ve s
how
s th
at A �
B�is
sh
orte
r th
an B�
C�.
Th
e st
atem
ent
on t
he
righ
t ab
ove
show
s th
at t
he
mea
sure
of
angl
e A
is l
ess
than
th
at o
f an
gle
B.
Th
ese
thre
e in
equ
alit
ies
are
tru
e fo
r an
y tr
ian
gle
AB
C,
no
mat
ter
how
lon
g th
e si
des.
a.A
B�
BC
�A
Cb
.If
AB
�A
C,t
hen
m�
C�
m�
B.
c.If
m�
C�
m�
B,t
hen
AB
�A
C.
Use
th
e th
ree
tria
ngl
e in
equ
alit
ies
for
thes
e p
rob
lem
s.
1.L
ist
the
side
s of
tri
angl
e D
EF
in o
rder
of
incr
easi
ng
len
gth
.
D�F�,
D�E�
,E�F�
2.In
th
e fi
gure
at
the
righ
t,w
hic
h l
ine
segm
ent
is t
he
shor
test
?
L�M�
3.E
xpla
in w
hy
the
len
gth
s 5
cm,1
0 cm
,an
d 20
cm
cou
ld n
ot b
e u
sed
to m
ake
a tr
ian
gle.
5 �
10 is
no
t g
reat
er t
han
20.
4.T
wo
side
s of
a t
rian
gle
mea
sure
3 i
n.a
nd
7 in
.Bet
wee
n w
hic
h t
wo
valu
es m
ust
th
e th
ird
side
be?
4 in
.an
d 1
0 in
.
5.In
tri
angl
e X
YZ
,XY
�15
,YZ
�12
,an
d X
Z�
9.W
hic
h i
s th
egr
eate
st a
ngl
e? W
hic
h i
s th
e le
ast?
�Z
;�
Y
6.L
ist
the
angl
es �
A,�
C,�
AB
C,a
nd
�A
BD
,in
ord
er o
f in
crea
sin
g si
ze.
�A
BD
,�A
,�A
BC
,�C
C ADB
13 1512
5 9
JM
K
L
65
60
65
55
65
50
D
FE
60
35
85
A
BC
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-1
6-1
Answers (Lesson 6-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g In
equ
alit
ies
by M
ult
iplic
atio
n a
nd
Div
isio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-2
6-2
©G
lenc
oe/M
cGra
w-H
ill34
9G
lenc
oe A
lgeb
ra 1
Lesson 6-2
Solv
e In
equ
alit
ies
by
Mu
ltip
licat
ion
If e
ach
sid
e of
an
in
equ
alit
y is
mu
ltip
lied
by
the
sam
e po
siti
ve n
um
ber,
the
resu
ltin
g in
equ
alit
y is
als
o tr
ue.
How
ever
,if
each
sid
e of
an
ineq
ual
ity
is m
ult
ipli
ed b
y th
e sa
me
neg
ativ
e n
um
ber,
the
dire
ctio
n o
f th
e in
equ
alit
y m
ust
be r
ever
sed
for
the
resu
ltin
g in
equ
alit
y to
be
tru
e.
For
all
num
bers
a,
b, a
nd c
, w
ith c
0,
1.if
cis
pos
itive
and
a�
b, t
hen
ac�
bc;
Mu
ltip
licat
ion
Pro
per
ty o
f In
equ
alit
ies
if c
is p
ositi
ve a
nd a
�b,
the
n ac
�bc
;
2.if
cis
neg
ativ
e an
d a
�b,
the
n ac
�bc
;if
cis
neg
ativ
e an
d a
�b,
the
n ac
�bc
.
Th
e pr
oper
ty i
s al
so t
rue
wh
en �
and
�ar
e re
plac
ed w
ith
�an
d �
.
Sol
ve �
�12
.
��
12O
rigin
al e
quat
ion
(�8)��
��(�
8)12
Mul
tiply
eac
h si
de b
y �
8; c
hang
e �
to �
.
y�
�96
Sim
plify
.
Th
e so
luti
on i
s {y
y�
�96
}.
y � 8y � 8
y � 8S
olve
k
�15
.
k�
15O
rigin
al e
quat
ion
��k
���
15M
ultip
ly e
ach
side
by
.
k�
20S
impl
ify.
Th
e so
luti
on i
s {k
k�
20}.
4 � 34 � 3
3 � 44 � 3
3 � 4
3 � 4Ex
ampl
e1Ex
ampl
e1Ex
ampl
e2Ex
ampl
e2
Exer
cises
Exer
cises
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on.
1.�
22.
��
223.
h�
�3
4.�
��
6
{yy
�12
}{n
n�
�11
00}
{hh
��
5}{p
p�
36}
5.n
�10
6.�
b�
7.�
�8.
�2.
51 �
�
{nn
�40
}�b
b�
��
�mm
��
�{h
h�
5.02
}
9.�
�2
10.�
��
11.
�5.
412
.�
�6
{gg
��
10}
�p p
��
{nn
�54
}{a
a�
�21
}
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.13
–15.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
13.H
alf
of a
nu
mbe
r is
at
leas
t 14
.n
�14
;{n
n�
28}
14.T
he
oppo
site
of
one-
thir
d a
nu
mbe
r is
gre
ater
th
an 9
.�
n�
9;{n
n�
�27
}
15.O
ne
fift
h o
f a
nu
mbe
r is
at
mos
t 30
.n
�30
;{n
n�
150}
1 � 5
1 � 3
1 � 25 � 12
2a � 7n � 10
9p � 53 � 4
g � 5
1 � 41 � 2
2h � 43 � 20
3m �5
1 � 32 � 3
1 � 4
p � 63 � 5
n � 50y � 6
©G
lenc
oe/M
cGra
w-H
ill35
0G
lenc
oe A
lgeb
ra 1
Solv
e In
equ
alit
ies
by
Div
isio
nIf
eac
h s
ide
of a
tru
e in
equ
alit
y is
div
ided
by
the
sam
e po
siti
ve n
um
ber,
the
resu
ltin
g in
equ
alit
y is
als
o tr
ue.
How
ever
,if
each
sid
e of
an
ineq
ual
ity
is d
ivid
ed b
y th
e sa
me
neg
ativ
e n
um
ber,
the
dire
ctio
n o
f th
e in
equ
alit
y sy
mbo
lm
ust
be
reve
rsed
for
th
e re
sult
ing
ineq
ual
ity
to b
e tr
ue.
For
all
num
bers
a,
b, a
nd c
with
c
0,
Div
isio
n P
rop
erty
1.if
cis
pos
itive
and
a�
b, t
hen
�;
if c
is p
ositi
ve a
nd a
�b,
the
n �
;o
f In
equ
alit
ies
2.if
cis
neg
ativ
e an
d a
�b,
the
n �
; if
cis
neg
ativ
e an
d a
�b,
the
n �
.
Th
e pr
oper
ty i
s al
so t
rue
wh
en �
and
�ar
e re
plac
ed w
ith
�an
d �
.
Sol
ve �
12y
�48
.
�12
y�
48O
rigin
al in
equa
lity
�D
ivid
e ea
ch s
ide
by �
12 a
nd c
hang
e �
to �
.
y�
�4
Sim
plify
.
Th
e so
luti
on i
s {y
y�
�4}
.
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on.
1.25
g�
�10
02.
�2x
�9
3.�
5c�
24.
�8m
��
64
{gg
��
4}�x
x�
�4
��c
c�
��
{mm
�8}
5.�
6k�
6.18
��
3b7.
30 �
�3n
8.�
0.24
�0.
6w
�k k
��
�{b
b�
�6}
{nn
��
10}
{ww
��
0.4}
9.25
��
2m10
.�30
��
5p11
.�2n
�6.
212
.�35
�0.
05h
�mm
��
12�
{pp
�6}
{nn
��
3.1}
{hh
��
700}
13.�
40 �
10h
14.�
n�
615
.�3
�
{hh
��
4}{n
n�
�9}
{pp
��
12}
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.16
–18.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
16.F
our
tim
es a
nu
mbe
r is
no
mor
e th
an 1
08.
4n�
108;
{nn
�27
}
17.T
he
oppo
site
of
thre
e ti
mes
a n
um
ber
is g
reat
er t
han
12.
�3n
�12
;{n
n�
�4}
18.N
egat
ive
five
tim
es a
nu
mbe
r is
at
mos
t 10
0.�
5n�
100;
{nn
��
20}
p � 42 � 3
1 � 2
1 � 30
1 � 5
2 � 51 � 2
48� �
12�
12y
� �12
b � ca � c
b � ca � c
b � ca � c
b � ca � c
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g In
equ
alit
ies
by M
ult
iplic
atio
n a
nd
Div
isio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-2
6-2
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 6-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
ract
ice
So
lvin
g In
equ
alit
ies
by M
ult
iplic
atio
n a
nd
Div
isio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-2
6-2
©G
lenc
oe/M
cGra
w-H
ill35
1G
lenc
oe A
lgeb
ra 1
Lesson 6-2
Mat
ch e
ach
in
equ
alit
y w
ith
its
cor
resp
ond
ing
stat
emen
t.
1.3n
�9
da.
Th
ree
tim
es a
nu
mbe
r is
at
mos
t n
ine.
2.n
�9
fb
.On
e th
ird
of a
nu
mbe
r is
no
mor
e th
an n
ine.
3.3n
�9
ac.
Neg
ativ
e th
ree
tim
es a
nu
mbe
r is
mor
e th
an n
ine.
4.�
3n�
9c
d.T
hre
e ti
mes
a n
um
ber
is l
ess
than
nin
e.
5.n
�9
be.
Neg
ativ
e th
ree
tim
es a
nu
mbe
r is
at
leas
t n
ine.
6.�
3n�
9e
f.O
ne
thir
d of
a n
um
ber
is g
reat
er t
han
or
equ
al t
o n
ine.
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on.
7.14
g�
568.
11w
�77
9.20
b�
�12
010
.�8r
�16
{gg
�4}
{ww
�7}
{bb
��
6}{r
r�
�2}
11.�
15p
��
9012
.�
913
.�
�15
14.�
��
9
{pp
�6}
{ss
�36
}{a
a�
�13
5}{p
p�
63}
15.�
�6
16.5
z�
�90
17.�
13m
��
2618
.�
�17
{tt
��
72}
{zz
��
18}
{mm
�2}
{kk
��
85}
19.�
y�
3620
.�16
c�
�22
421
.��
222
.12
�
{yy
��
36}
{cc
�14
}{h
h�
�20
}{d
d�
144}
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.23
–27.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
23.F
our
tim
es a
nu
mbe
r is
gre
ater
th
an �
48.
4n�
�48
;{n
n�
�12
}
24.O
ne
eigh
th o
f a
nu
mbe
r is
les
s th
an o
r eq
ual
to
3.n
�3;
{nn
�24
}
25.N
egat
ive
twel
ve t
imes
a n
um
ber
is n
o m
ore
than
84.
�12
n�
84;
{nn
��
7}
26.N
egat
ive
one
sixt
h o
f a
nu
mbe
r is
les
s th
an �
9.�
n�
�9;
{nn
�54
}
27.E
igh
t ti
mes
a n
um
ber
is a
t le
ast
16.
8n�
16;
{nn
�2}
1 � 61 � 8
d � 12h � 10
k � 5t
� 12
p � 7a � 9
s � 4
1 � 31 � 3
©G
lenc
oe/M
cGra
w-H
ill35
2G
lenc
oe A
lgeb
ra 1
Mat
ch e
ach
in
equ
alit
y w
ith
its
cor
resp
ond
ing
stat
emen
t.
1.�
4n�
5d
a.N
egat
ive
fou
r ti
mes
a n
um
ber
is l
ess
than
fiv
e.
2.n
�5
fb
.Fou
r fi
fth
s of
a n
um
ber
is n
o m
ore
than
fiv
e.
3.4n
�5
ec.
Fou
r ti
mes
a n
um
ber
is f
ewer
th
an f
ive.
4.n
�5
bd
.Neg
ativ
e fo
ur
tim
es a
nu
mbe
r is
no
less
th
an f
ive.
5.4n
�5
ce.
Fou
r ti
mes
a n
um
ber
is a
t m
ost
five
.
6.�
4n�
5a
f.F
our
fift
hs
of a
nu
mbe
r is
mor
e th
an f
ive.
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on.
7.�
��
148.
�13
h�
529.
��
610
.39
�13
p
{aa
�70
}{h
h�
�4}
{ss
��
96}
{pp
�3}
11.
n�
�12
12.�
t�
2513
.�m
��
614
.k
��
10
{nn
��
18}
{tt
��
45}
{mm
�10
}{k
k�
�3}
15.�
3b�
0.75
16.�
0.9c
��
917
.0.1
x�
�4
18.�
2.3
�
{bb
��
0.25
}{c
c�
10}
{xx
��
40}
{jj
��
9.2}
19.�
15y
�3
20.2
.6v
��
20.8
21.0
��
0.5u
22.
f�
�1
�y y
��
�{v
v�
�8}
{uu
�0}
�f f
��
�D
efin
e a
vari
able
,wri
te a
n i
neq
ual
ity,
and
sol
ve e
ach
pro
ble
m.T
hen
ch
eck
you
rso
luti
on.
23�
25.S
amp
le a
nsw
er:
Let
n�
the
nu
mb
er.
23.N
egat
ive
thre
e ti
mes
a n
um
ber
is a
t le
ast
57.
�3n
�57
;{n
n�
�19
}
24.T
wo
thir
ds o
f a
nu
mbe
r is
no
mor
e th
an �
10.
n�
�10
;{n
n�
�15
}
25.N
egat
ive
thre
e fi
fth
s of
a n
um
ber
is l
ess
than
�6.
�n
��
6;{n
n�
10}
26.F
LOO
DIN
GA
riv
er i
s ri
sin
g at
a r
ate
of 3
in
ches
per
hou
r.If
th
e ri
ver
rise
s m
ore
than
2fe
et,i
t w
ill
exce
ed f
lood
sta
ge.H
ow l
ong
can
th
e ri
ver
rise
at
this
rat
e w
ith
out
exce
edin
gfl
ood
stag
e?n
o m
ore
th
an 8
h
27.S
ALE
SP
et S
upp
lies
mak
es a
pro
fit
of $
5.50
per
bag
on
its
lin
e of
nat
ura
l do
g fo
od.I
f th
est
ore
wan
ts t
o m
ake
a pr
ofit
of
no
less
th
an $
5225
,how
man
y ba
gs o
f do
g fo
od d
oes
itn
eed
to s
ell?
at le
ast
950
bag
s
3 � 5
2 � 3
8 � 71 � 5
7 � 8
j � 4
10 � 33 � 5
5 � 92 � 3
s � 16a � 5
4 � 54 � 5
Pra
ctic
e (
Ave
rag
e)
So
lvin
g In
equ
alit
ies
by M
ult
iplic
atio
n a
nd
Div
isio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-2
6-2
Answers (Lesson 6-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csS
olv
ing
Ineq
ual
itie
s by
Mu
ltip
licat
ion
an
d D
ivis
ion
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-2
6-2
©G
lenc
oe/M
cGra
w-H
ill35
3G
lenc
oe A
lgeb
ra 1
Lesson 6-2
Pre-
Act
ivit
yW
hy
are
ineq
ual
itie
s im
por
tan
t in
lan
dsc
apin
g?
Rea
d th
e in
trod
uct
ion
to
Les
son
6-2
at
the
top
of p
age
325
in y
our
text
book
.
•W
ould
a w
all
6 br
icks
hig
h b
e lo
wer
th
an a
wal
l 6
bloc
ks h
igh
? W
hy?
yes;
6(3)
�6(
12)
•W
ould
a w
all
nbr
icks
hig
h b
e lo
wer
th
an a
wal
l n
bloc
ks h
igh
? E
xpla
in.
yes;
Wh
en o
ne
qu
anti
ty is
less
th
an a
no
ther
qu
anti
ty,
mu
ltip
lyin
g b
oth
qu
anti
ties
by
the
sam
e p
osi
tive
nu
mb
erd
oes
no
t ch
ang
e th
e tr
uth
of
the
ineq
ual
ity.
Rea
din
g t
he
Less
on
1.W
rite
an
in
equ
alit
y th
at d
escr
ibes
eac
h s
itu
atio
n.
a.A
nu
mbe
r n
divi
ded
by 8
is
grea
ter
than
5.
n
8 �
5
b.
Tw
elve
tim
es a
nu
mbe
r k
is a
t le
ast
7.12
k�
7
c.A
nu
mbe
r x
divi
ded
by �
10 i
s le
ss t
han
or
equ
al t
o 50
.x
(�
10)
�50
d.
Th
ree
fift
hs
of a
nu
mbe
r n
is a
t m
ost
13.
n�
13
e.N
ine
is g
reat
er t
han
or
equ
al t
o on
e h
alf
of a
qu
anti
ty m
.9
�m
2.U
se w
ords
to
tell
wh
at e
ach
in
equ
alit
y sa
ys.
a.12
�6n
12 is
less
th
an 6
tim
es a
nu
mb
er n
.
b.
�14
A n
um
ber
td
ivid
ed b
y �
3 is
gre
ater
th
an o
r eq
ual
to
14.
c.11
x�
3211
tim
es a
nu
mb
er x
is a
t m
ost
32.
Hel
pin
g Y
ou
Rem
emb
er
3.In
you
r ow
n w
ords
,wri
te a
ru
le f
or m
ult
iply
ing
and
divi
din
g in
equ
alit
ies
by p
osit
ive
and
neg
ativ
e n
um
bers
.
Sam
ple
an
swer
:Wh
en y
ou
mu
ltip
ly o
r d
ivid
e ea
ch s
ide
of
a tr
ue
ineq
ual
ity
by a
po
siti
ve n
um
ber
,th
e re
sult
is t
rue.
Wh
en y
ou
mu
ltip
ly o
rd
ivid
e a
tru
e in
equ
alit
y by
a n
egat
ive
nu
mb
er,y
ou
mu
st r
ever
se t
he
dir
ecti
on
of
the
ineq
ual
ity
sig
n.
t� �
3
1 � 2
3 � 5
©G
lenc
oe/M
cGra
w-H
ill35
4G
lenc
oe A
lgeb
ra 1
Th
e M
aya
'I'h
e M
aya
wer
e a
Nat
ive
Am
eric
an p
eopl
e w
ho
live
d fr
om a
bou
t15
00 B
.C.t
o ab
out
1500
A.D
.in
th
e re
gion
th
at t
oday
en
com
pass
esm
uch
of
Cen
tral
Am
eric
a an
d so
uth
ern
Mex
ico.
Th
eir
man
yac
com
plis
hm
ents
in
clu
de e
xcep
tion
al a
rch
itec
ture
,pot
tery
,pa
inti
ng,
and
scu
lptu
re,a
s w
ell
as s
ign
ific
ant
adva
nce
s in
th
efi
elds
of
astr
onom
y an
d m
ath
emat
ics.
Th
e M
aya
deve
lope
d a
syst
em o
f n
um
erat
ion
th
at w
as b
ased
on
the
nu
mbe
r tw
enty
.Th
e ba
sic
sym
bols
of
this
sys
tem
are
sh
own
in
the
tabl
e at
th
e ri
ght.
Th
e pl
aces
in
a M
ayan
nu
mer
al a
re w
ritt
enve
rtic
ally
—th
e bo
ttom
pla
ce r
epre
sen
ts o
nes
,th
e pl
ace
abov
ere
pres
ents
tw
enti
es,t
he
plac
e ab
ove
that
rep
rese
nts
20
20
,or
fou
r h
un
dre
ds,
and
so o
n.F
or i
nst
ance
,th
is i
s h
ow t
o w
rite
th
en
um
ber
997
in M
ayan
nu
mer
als.
←2
�
800
←9
�
180
←17
�
17 997
Eva
luat
e ea
ch e
xpre
ssio
n w
hen
v�
,w�
,x�
,y�
,an
d
z�
.Th
en w
rite
th
e an
swer
in
May
an n
um
eral
s.E
xerc
ise
5 is
don
e fo
r yo
u.
1.2.
3.xv
4.vx
y5.
wx
�z
6.vz
�xy
7.w
(v�
x �
z)8.
vwz
9.z(
wx
�x)
Tel
l w
het
her
eac
h s
tate
men
t is
tru
eor
fa
lse.
10.
��
�11
.�
12.
�
tru
efa
lse
fals
e
13.(
�)
��
�(
�)
tru
e
14.H
ow a
re E
xerc
ises
10
and
11 a
like
? H
ow a
re t
hey
dif
fere
nt?
Bo
th in
volv
e ch
ang
ing
th
e o
rder
of
the
sym
bo
ls. E
xerc
ise
10 in
volv
esch
ang
ing
th
e o
rder
of
the
add
end
s in
an
ad
dit
ion
pro
ble
m. E
xerc
ise
11in
volv
es c
han
gin
g t
he
ord
er o
f th
e d
igit
s in
a n
um
eral
.
____
___
___
____
_•
• •
____
___
___
____
_•
• •
• •
•__
___
____
___
___
____
_•
• •
____
___
___
____
_
•__
___
• •
•__
___
____
_
• •
•__
___
____
_
•__
___
• •
•__
___
____
_•
____
_•
____
_•
• •
____
___
___
• •
●●●● •__
___
____
___
___
• •
••
• •
••
____
___
___
____
_
• •
• •
____
___
___
____
_
•__
___
____
___
___
• •
••
•__
___
____
_•
• •
●●●●
●●●●
••
• •
•
• •
• •
____
_v
�w
�z
�� x
• •
•z � w
• •
____
___
___
●●●●•
• •
••
• •
____
___
___
____
_•
____
_
1•
•__
___
____
___
___
20•
• •
•__
___
400
• •
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-2
6-2
010
111
212
313
414
515
616
717
818
919
• •
• •
____
___
___
____
_•
• •
•__
___
• •
• __
___
____
___
___
• •
•__
___
• •
____
___
___
____
_•
•__
___
•__
___
____
___
___
•__
___
____
___
___
____
___
___
• •
• •
____
___
___
• •
• •
• •
•__
___
____
_•
• •
• •
____
___
___
• •
•__
___
____
_•
____
___
___
●●●●
Answers (Lesson 6-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g M
ult
i-S
tep
Ineq
ual
itie
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-3
6-3
©G
lenc
oe/M
cGra
w-H
ill35
5G
lenc
oe A
lgeb
ra 1
Lesson 6-3
Solv
e M
ult
i-St
ep In
equ
alit
ies
To
solv
e li
nea
r in
equ
alit
ies
invo
lvin
g m
ore
than
on
eop
erat
ion
,un
do t
he
oper
atio
ns
in r
ever
se o
f th
e or
der
of o
pera
tion
s,ju
st a
s yo
u w
ould
sol
vean
equ
atio
n w
ith
mor
e th
an o
ne
oper
atio
n.
Sol
ve 6
x�
4 �
2x�
12.
6x�
4 �
2x�
12O
rigin
al in
equa
lity
6x�
4 �
2x�
2x�
12 �
2xS
ubtr
act
2xfr
om
each
sid
e.
4x�
4 �
12S
impl
ify.
4x�
4 �
4 �
12 �
4A
dd 4
to
each
sid
e.
4x�
16S
impl
ify.
�D
ivid
e ea
ch s
ide
by 4
.
x�
4S
impl
ify.
Th
e so
luti
on i
s {x
x�
4}.
16 � 44x � 4
Sol
ve 3
a�
15 �
4 �
5a.
3a�
15 �
4 �
5aO
rigin
al in
equa
lity
3a�
15 �
5a�
4 �
5a�
5aS
ubtr
act
5afr
om
each
sid
e.
�2a
�15
�4
Sim
plify
.
�2a
�15
�15
�4
�15
Add
15
to e
ach
side
.
�2a
�19
Sim
plify
.
�D
ivid
e ea
ch s
ide
by �
2
and
chan
ge �
to �
.
a�
�9
Sim
plify
.
Th
e so
luti
on i
s �a
a�
�9
�.1 � 2
1 � 2
19 � �2
�2a
� �2
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on.
1.11
y�
13 �
�1
2.8n
�10
�6
�2n
3.�
1 �
�5
�y y
��
1�
�n n
�1
�{q
q�
�42
}
4.6n
�12
�8
�8n
5.�
12 �
d�
�12
�4d
6.5r
�6
�8r
�18
{nn
�2}
{dd
�0}
{rr
�4}
7.�
128.
7.3y
�14
.4 �
4.9y
9.�
8m�
3 �
18 �
m
{xx
��
6}{y
y�
6}{m
m�
�3}
10.�
4y�
10 �
19 �
2y11
.9n
�24
n�
45 �
012
.�
�4
�y y
��
14�
{nn
�3}
�x x
��
4�
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.13
–15.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
13.N
egat
ive
thre
e ti
mes
a n
um
ber
plu
s fo
ur
is n
o m
ore
than
th
e n
um
ber
min
us
eigh
t.�
3n�
4 �
n�
8;{n
n�
3}
14.O
ne
fou
rth
of
a n
um
ber
decr
ease
d by
th
ree
is a
t le
ast
two.
n�
3 �
2;{n
n�
20}
15.T
he
sum
of
twel
ve a
nd
a n
um
ber
is n
o gr
eate
r th
an t
he
sum
of
twic
e th
e n
um
ber
and
�8.
12 �
n�
2n�
(�8)
;{n
n�
20}
1 � 4
1 � 21 � 2
4x�
2�
5
�3x
�6
�� 2
3 � 53 � 11
q � 7
©G
lenc
oe/M
cGra
w-H
ill35
6G
lenc
oe A
lgeb
ra 1
Solv
e In
equ
alit
ies
Invo
lvin
g t
he
Dis
trib
uti
ve P
rop
erty
Wh
en s
olvi
ng
ineq
ual
itie
s th
at c
onta
in g
rou
pin
g sy
mbo
ls,f
irst
use
th
e D
istr
ibu
tive
Pro
pert
y to
rem
ove
the
grou
pin
g sy
mbo
ls.T
hen
un
do t
he
oper
atio
ns
in r
ever
se o
f th
e or
der
of o
pera
tion
s,ju
st a
s yo
uw
ould
sol
ve a
n e
quat
ion
wit
h m
ore
than
on
e op
erat
ion
.
Sol
ve 3
a�
2(6a
�4)
�4
�(4
a�
6).
3a�
2(6a
�4)
�4
�(4
a�
6)O
rigin
al in
equa
lity
3a�
12a
�8
�4
�4a
�6
Dis
trib
utiv
e P
rope
rty
�9a
�8
��
2 �
4aC
ombi
ne li
ke t
erm
s.
�9a
�8
�4a
��
2 �
4a�
4aA
dd 4
ato
eac
h si
de.
�5a
�8
��
2C
ombi
ne li
ke t
erm
s.
�5a
�8
�8
��
2 �
8S
ubtr
act
8 fr
om e
ach
side
.
�5a
��
10S
impl
ify.
a�
2D
ivid
e ea
ch s
ide
by �
5 an
d ch
ange
�to
�.
Th
e so
luti
on i
n s
et-b
uil
der
not
atio
n i
s {a
a�
2}.
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on.
1.2(
t�
3) �
162.
3(d
�2)
�2d
�16
3.4h
�8
�2(
h�
1)
{tt
�5}
{dd
�22
}{h
h�
3}
4.6y
�10
�8
�(y
�14
)5.
4.6(
x�
3.4)
�5.
1x6.
�5x
�(2
x�
3) �
1
�y y
��
2�
{xx
��
31.2
8}�x
x�
��
7.3(
2y�
4) �
2(y
�1)
�10
8.8
�2(
b�
1) �
12 �
3b9.
�2(
k�
1) �
8(1�
k)
{yy
�6}
{bb
�6}
�k k
��
�10
.0.3
(y�
2) �
0.4(
1 �
y)11
.m�
17 �
�(4
m�
13)
{yy
��
10}
�mm
��
�12
.3n
�8
�2(
n�
4) �
2(1
�n
)13
.2(y
�2)
��
4 �
2y
{nn
�18
}�
14.k
�17
��
(17
�k)
15.n
�4
��
3(2
�n
)
{kk
is a
rea
l nu
mb
er}
�n n
��
�D
efin
e a
vari
able
,wri
te a
n i
neq
ual
ity,
and
sol
ve e
ach
pro
ble
m.T
hen
ch
eck
you
rso
luti
on.
16–1
8.S
amp
le a
nsw
er:
Let
n�
the
nu
mb
er.
16.T
wic
e th
e su
m o
f a
nu
mbe
r an
d 4
is l
ess
than
12.
2(n
�4)
�12
;{n
n�
2}
17.T
hre
e ti
mes
th
e su
m o
f a
nu
mbe
r an
d si
x is
gre
ater
th
an f
our
tim
es t
he
nu
mbe
rde
crea
sed
by t
wo.
3(n
�6)
�4n
�2;
{nn
�20
}
18.T
wic
e th
e di
ffer
ence
of
a n
um
ber
and
fou
r is
les
s th
an t
he
sum
of
the
nu
mbe
r an
d fi
ve.
2(n
�4)
�n
�5;
{nn
�13
}
1 � 2
4 � 5
3 � 54 � 72 � 7
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g M
ult
i-S
tep
Ineq
ual
itie
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-3
6-3
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 6-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
So
lvin
g M
ult
i-S
tep
Ineq
ual
itie
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-3
6-3
©G
lenc
oe/M
cGra
w-H
ill35
7G
lenc
oe A
lgeb
ra 1
Lesson 6-3
Ju
stif
y ea
ch i
nd
icat
ed s
tep
.
1.t
�3
��
15
t�
3 �
3 �
�15
�3
a.
t�
�12
��t�
(�12
)b
.
t�
�16
a.A
dd
3 t
o e
ach
sid
e.b
.Mu
ltip
ly e
ach
sid
e by
.
2.5(
k�
8) �
7 �
235k
�40
�7
�23
a.5k
�33
�23
5k�
33 �
33 �
23 �
33b
.5k
��
10
�c.
k�
�2
a.D
istr
ibu
tive
Pro
per
tyb
.Su
btr
act
33 f
rom
eac
h s
ide.
c.D
ivid
e ea
ch s
ide
by 5
.
?�
10�
55k � 5
??
4 � 3
?4 � 3
3 � 44 � 3
3 � 4
?3 � 4
3 � 4
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on.
3.�
2b�
4 �
�6
4.3x
�15
�21
5.�
1 �
3
{bb
�5}
{xx
�2}
{dd
�8}
6.a
�4
�2
7.�
�7
��
48.
j�
10 �
5
{aa
�15
}{t
t�
55}
{jj
�20
}
9.�
f�
3 �
�9
10.2
p�
5 �
3p�
1011
.4k
�15
��
2k�
3
{ff
�18
}{p
p�
15}
{kk
��
2}
12.2
(�3m
�5)
��
2813
.�6(
w�
1) �
2(w
�5)
14.2
(q�
3) �
6 �
�10
{mm
�3}
{ww
��
2}{q
q�
�5}
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.15
–20.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
15.F
our
mor
e th
an t
he
quot
ien
t of
a n
um
ber
and
thre
e is
at
leas
t n
ine.
�4
�9;
{ nn
�15
}
16.T
he
sum
of
a n
um
ber
and
fou
rtee
n i
s le
ss t
han
or
equ
al t
o th
ree
tim
es t
he
nu
mbe
r.n
�14
�3n
;{n
n�
7}
17.N
egat
ive
thre
e ti
mes
a n
um
ber
incr
ease
d by
sev
en i
s le
ss t
han
neg
ativ
e el
even
.�
3n�
7 �
�11
;{n
n�
6}
18.F
ive
tim
es a
nu
mbe
r de
crea
sed
by e
igh
t is
at
mos
t te
n m
ore
than
tw
ice
the
nu
mbe
r.5n
�8
�2n
�10
;{n
n�
6}
19.S
even
mor
e th
an f
ive
sixt
hs
of a
nu
mbe
r is
mor
e th
an n
egat
ive
thre
e.n
�7
��
3;{ n
n�
�12
}
20.F
our
tim
es t
he
sum
of
a n
um
ber
and
two
incr
ease
d by
th
ree
is a
t le
ast
twen
ty-s
even
.4(
n�
2) �
3 �
27;
{nn
�4}
5 � 6
n � 3
2 � 3
3 � 4t � 5
2 � 5
d � 2
©G
lenc
oe/M
cGra
w-H
ill35
8G
lenc
oe A
lgeb
ra 1
Ju
stif
y ea
ch i
nd
icat
ed s
tep
.
Pra
ctic
e (
Ave
rag
e)
So
lvin
g M
ult
i-S
tep
Ineq
ual
itie
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-3
6-3
1.x
�
8x�
(8)
a.
8x�
5x�
128x
�5x
�5x
�12
�5x
b.
3x�
�12
�c.
x�
�4
a.M
ult
iply
eac
h s
ide
by 8
.b
.Su
btr
act
5 xfr
om
eac
h s
ide.
c.D
ivid
e ea
ch s
ide
by 3
.
2.2(
2h�
2) �
2(3h
�5)
�12
4h�
4 �
6h�
10 �
12a.
4h�
4 �
6h�
24h
�4
�6h
�6h
�2
�6h
b.
�2h
�4
��
2�
2h�
4 �
4 �
�2
�4
c.�
2h�
�6
�d
.
h�
3a.
Dis
trib
uti
ve P
rop
erty
b.S
ub
trac
t 6 h
fro
m e
ach
sid
e.c.
Su
btr
act
4 fr
om
eac
h s
ide.
d.D
ivid
e ea
ch s
ide
by �
2 an
dch
ang
e �
to �
.
?�
6� �
2�
2h� �
2
???
?�
12�
33x � 3
??5x
�12
�8
5x�
12�
8
Sol
ve e
ach
in
equ
alit
y.T
hen
ch
eck
you
r so
luti
on.
3.�
5 �
��
94.
4u�
6 �
6u�
205.
13 �
a�
1
{tt
�24
}{u
u�
7}{a
a�
21}
6.�
�8
{ww
��
19}
7.�
7{f
f�
15}
8.h
�{h
h�
�3}
9.3(
z�
1) �
11 �
�2(
z�
13)
{zz
��
8}
10.3
e�
2(4e
�2)
�2(
6e�
1){e
e�
2}11
.5n
�3(
n�
6) �
0{n
n�
�9}
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.12
–13.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
12.A
nu
mbe
r is
les
s th
an o
ne
fou
rth
th
e su
m o
f th
ree
tim
es t
he
nu
mbe
r an
d fo
ur.
n�
;{n
n�
4}13
.Tw
o ti
mes
th
e su
m o
f a
nu
mbe
r an
d fo
ur
is n
o m
ore
than
th
ree
tim
es t
he
sum
of
the
nu
mbe
r an
d se
ven
dec
reas
ed b
y fo
ur.
2(n
�4)
�3(
n�
7) �
4;{n
n�
�9}
14.G
EOM
ETRY
Th
e ar
ea o
f a
tria
ngu
lar
gard
en c
an b
e n
o m
ore
than
120
squ
are
feet
.Th
eba
se o
f th
e tr
ian
gle
is 1
6 fe
et.W
hat
is
the
hei
ght
of t
he
tria
ngl
e?n
o m
ore
th
an 1
5 ft
15.M
USI
C P
RA
CTI
CE
Nab
uko
pra
ctic
es t
he
viol
in a
t le
ast
12 h
ours
per
wee
k.S
he
prac
tice
s fo
r th
ree
fou
rth
s of
an
hou
r ea
ch s
essi
on.I
f N
abu
ko h
as a
lrea
dy p
ract
iced
3
hou
rs i
n o
ne
wee
k,h
ow m
any
sess
ion
s re
mai
n t
o m
eet
or e
xcee
d h
er w
eekl
y pr
acti
ce g
oal?
at le
ast
12 s
essi
on
s
3n�
4�
4
6h�
3�
5
3f�
10�
5w
�3
�2
2 � 3t � 6
Answers (Lesson 6-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
olv
ing
Mu
lti-
Ste
p In
equ
alit
ies
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-3
6-3
©G
lenc
oe/M
cGra
w-H
ill35
9G
lenc
oe A
lgeb
ra 1
Lesson 6-3
Pre-
Act
ivit
yH
ow a
re l
inea
r in
equ
alit
ies
use
d i
n s
cien
ce?
Rea
d th
e in
trod
uct
ion
to
Les
son
6-3
at
the
top
of p
age
332
in y
our
text
book
.T
hen
wri
te a
n i
neq
ual
ity
that
cou
ld b
e u
sed
to f
ind
the
tem
pera
ture
s in
degr
ees
Cel
siu
s fo
r w
hic
h e
ach
su
bsta
nce
is
a ga
s.
Arg
on:
C�
32 �
�30
3B
rom
ine:
C�
32 �
138
Rea
din
g t
he
Less
on
1.W
hat
does
the
phr
ase
“und
oing
the
ope
rati
ons
in r
ever
se o
f th
e or
der
of o
pera
tion
s”m
ean?
Sam
ple
an
swer
:F
irst
ad
d o
r su
btr
act
to u
nd
o s
ub
trac
tio
n o
r ad
dit
ion
,th
en m
ult
iply
or
div
ide
to u
nd
o d
ivis
ion
or
mu
ltip
licat
ion
.
2.D
escr
ibe
how
ch
ecki
ng
the
solu
tion
of
an i
neq
ual
ity
is d
iffe
ren
t fr
om c
hec
kin
g th
eso
luti
on o
f an
equ
atio
n.
Sam
ple
an
swer
:In
stea
d o
f su
bst
itu
tin
g o
ne
valu
e fo
r th
e va
riab
le,t
her
ear
e in
fin
itel
y m
any
valu
es t
hat
can
be
use
d t
o c
hec
k.It
is a
go
od
idea
to
use
a v
alu
e th
at is
less
th
an,t
he
valu
e eq
ual
to
,an
d a
val
ue
gre
ater
th
anth
e n
um
ber
in t
he
solu
tio
n t
o c
hec
k an
ineq
ual
ity.
3.D
escr
ibe
how
th
e D
istr
ibu
tive
Pro
pert
y ca
n b
e u
sed
to r
emov
e th
e gr
oupi
ng
sym
bols
in
the
ineq
ual
ity
4x�
7(2x
�8)
�3x
�5.
Mu
ltip
ly �
7 by
bo
th 2
xan
d 8
.
4.Is
it
poss
ible
to
hav
e n
o so
luti
on w
hen
you
sol
ve a
n i
neq
ual
ity?
Exp
lain
you
r an
swer
an
dgi
ve a
n e
xam
ple.
Sam
ple
an
swer
:Yes
;if
so
lvin
g r
esu
lts
in a
n in
equ
alit
y th
at is
nev
er t
rue
(an
d t
he
sig
ns
hav
e b
een
rev
erse
d if
nec
essa
ry),
then
th
ere
is n
oso
luti
on
.Exa
mp
le:
3(t
�4)
�8
�3
(t�
4) �
8
Hel
pin
g Y
ou
Rem
emb
er
5.M
ake
a ch
eckl
ist
of s
teps
you
can
use
wh
en s
olvi
ng
ineq
ual
itie
s.
(1)
Use
th
e D
istr
ibu
tive
Pro
per
ty t
o r
emov
e an
y g
rou
pin
g s
ymb
ols
.(2
)C
om
bin
e an
y lik
e te
rms.
(3)
Ad
d o
r su
btr
act
the
sam
e va
riab
le t
erm
s o
r co
nst
ants
on
bo
th s
ides
.(4
)M
ult
iply
or
div
ide
to u
nd
o o
per
atio
ns.
(5)
Rev
erse
th
e d
irec
tio
n o
f th
e in
equ
alit
y sy
mb
ol i
f b
oth
sid
es w
ere
mu
ltip
lied
or
div
ided
by
a n
egat
ive
nu
mb
er.
(6)
Be
sure
th
e va
riab
le is
by
itse
lf o
n o
ne
sid
e o
f th
e fi
nal
ineq
ual
ity.
9 � 59 � 5
©G
lenc
oe/M
cGra
w-H
ill36
0G
lenc
oe A
lgeb
ra 1
Car
los
Mo
nte
zum
a D
uri
ng
his
lif
etim
e,C
arlo
s M
onte
zum
a (1
865?
–192
3) w
as o
ne
of t
he
mos
t in
flu
enti
al N
ativ
e A
mer
ican
s in
th
e U
nit
ed S
tate
s.H
e w
asre
cogn
ized
as
a pr
omin
ent
phys
icia
n a
nd
was
als
o a
pass
ion
ate
advo
cate
of t
he
righ
ts o
f N
ativ
e A
mer
ican
peo
ples
.Th
e ex
erci
ses
that
fol
low
wil
lh
elp
you
lea
rn s
ome
inte
rest
ing
fact
s ab
out
Dr.
Mon
tezu
ma’
s li
fe.
Sol
ve e
ach
in
equ
alit
y.T
he
wor
d o
r p
hra
se n
ext
to t
he
equ
ival
ent
ineq
ual
ity
wil
l co
mp
lete
th
e st
atem
ent
corr
ectl
y.
1.�
2k�
102.
5 �
r�
9 M
onte
zum
a w
as b
orn
in
th
e st
ate
He
was
a N
ativ
e A
mer
ican
of
the
of
.Ya
vapa
is,w
ho
are
a pe
ople
.
a.k
��
5A
rizo
na
a.r
��
4N
avaj
o
b.
k�
�5
Mon
tan
ab
.r
��
4M
ohaw
k
c.k
�12
Uta
hc.
r�
14M
ohav
e-A
pach
e
3.�
y�
�9
4.�
3 �
q�
12
Mon
tezu
ma
rece
ived
a m
edic
alA
s a
phys
icia
n,M
onte
zum
a's
fiel
d of
de
gree
fro
m
in 1
889.
spec
iali
zati
on w
as
.
a.y
�9
Ch
icag
o M
edic
al C
olle
gea.
q�
�4
hea
rt s
urg
ery
b.
y�
�9
Har
vard
Med
ical
Sch
ool
b.
q�
15in
tern
al m
edic
ine
c.y
�9
Joh
ns
Hop
kin
s U
niv
ersi
tyc.
q�
�15
resp
irat
ory
dise
ases
5.5
�4x
�14
�x
6.7
�t
�7
�t
For
mu
ch o
f h
is c
aree
r,h
e m
ain
tain
ed
In a
ddit
ion
to
mai
nta
inin
g h
is m
edic
ala
med
ical
pra
ctic
e in
.
prac
tice
,he
was
als
o a(
n)
.
a.x
�9
New
Yor
k C
ity
a.t
�7
dire
ctor
of
a bl
ood
ban
k
b.
x�
3C
hic
ago
b.
t�
0in
stru
ctor
at
a m
edic
al c
olle
ge
c.x
��
9B
osto
nc.
t�
�7
lega
l co
un
sel
to p
hys
icia
ns
7.3a
�8
�4a
�10
8.6n
�8n
�12
M
onte
zum
a fo
un
ded,
wro
te,a
nd
Mon
tezu
ma
test
ifie
d be
fore
a
edit
ed
,a m
onth
ly n
ewsl
ette
rco
mm
itte
e of
th
e U
nit
ed S
tate
s th
at a
ddre
ssed
Nat
ive
Am
eric
anC
ongr
ess
con
cern
ing
his
wor
k in
co
nce
rns.
trea
tin
g .
a.a
��
2Ya
vapa
ia.
n�
6ap
pen
dici
tis
b.
a�
18A
pach
eb
.n
��
6as
thm
a
c.a
�18
Was
saja
c.n
��
10h
eart
att
acks
?
?
??
??
??
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-3
6-3
Answers (Lesson 6-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g C
om
po
un
d In
equ
alit
ies
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-4
6-4
©G
lenc
oe/M
cGra
w-H
ill36
1G
lenc
oe A
lgeb
ra 1
Lesson 6-4
Ineq
ual
itie
s C
on
tain
ing
an
dA
com
pou
nd
ineq
ual
ity
con
tain
ing
and
is t
rue
only
if
both
in
equ
alit
ies
are
tru
e.T
he
grap
h o
f a
com
pou
nd
ineq
ual
ity
con
tain
ing
and
is t
he
inte
rsec
tion
of t
he
grap
hs
of t
he
two
ineq
ual
itie
s.E
very
sol
uti
on o
f th
e co
mpo
un
din
equ
alit
y m
ust
be
a so
luti
on o
f bo
th i
neq
ual
itie
s.
Gra
ph
th
e so
luti
onse
t of
x�
2 an
d x
��
1. Gra
ph x
�2.
Gra
ph x
��
1.
Fin
d th
e in
ters
ectio
n.
Th
e so
luti
on s
et i
s {x
�1
�x
�2}
.
�2
�1
�3
01
23
�3
�2
�1
01
23
�3
�2
�1
01
23
Sol
ve �
1 �
x�
2 �
3 u
sin
ga
nd
.Th
en g
rap
h t
he
solu
tion
set
.
�1
�x
�2
and
x�
2 �
3�
1 �
2 �
x�
2 �
2x
�2
�2
�3
�2
�3
�x
x�
1
Gra
ph x
��
3.
Gra
ph x
�1.
Fin
d th
e in
ters
ectio
n.
Th
e so
luti
on s
et i
s {x
�3
�x
�1}
.
�2
�1
�4
�3
01
2
�3
�4
�2
�1
01
2
�3
�4
�2
�1
01
2
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Gra
ph
th
e so
luti
on s
et o
f ea
ch c
omp
oun
d i
neq
ual
ity.
1.b
��
1 an
d b
�3
2.2
�q
��
53.
x�
�3
and
x�
4
4.�
2 �
p�
45.
�3
�d
and
d�
26.
�1
�p
�3
Sol
ve e
ach
com
pou
nd
in
equ
alit
y.T
hen
gra
ph
th
e so
luti
on s
et.
7.4
�w
�3
�5
8.�
3 �
p�
5 �
2{w
1 �
w�
2}{p
2 �
p�
7}
9.�
4 �
x�
2 �
�2
10.y
�1�
2 an
d y
�2
�1
{x�
6 �
x�
�4}
{y�
1 �
y�
3}
11.n
�2
��
3 an
d n
�4
�6
12.d
�3
�6d
�12
�2d
�32
{n�
1 �
n�
2}{d
�3
�d
�5}
�3
�2
�1
01
23
45
�3
�4
�2
�1
01
23
4
�3
�4
�2
�1
01
23
4�
7�
6�
5�
4�
3�
2�
10
1
01
23
45
67
8�
3�
4�
2�
10
12
34
�3
�4
�2
�1
01
23
4�
3�
4�
2�
10
12
34
�3
�2
�1
01
23
45
�4
�3
�2
�1
01
23
4�
4�
3�
6�
5�
2�
10
12
�4
�3
�2
�1
01
23
4
©G
lenc
oe/M
cGra
w-H
ill36
2G
lenc
oe A
lgeb
ra 1
Ineq
ual
itie
s C
on
tain
ing
or
A c
ompo
un
d in
equ
alit
y co
nta
inin
g or
is t
rue
if o
ne
orbo
th o
f th
e in
equ
alit
ies
are
tru
e.T
he
grap
h o
f a
com
pou
nd
ineq
ual
ity
con
tain
ing
oris
th
eu
nio
nof
th
e gr
aph
s of
th
e tw
o in
equ
alit
ies.
Th
e u
nio
n c
an b
e fo
un
d by
gra
phin
g bo
thin
equ
alit
ies
on t
he
sam
e n
um
ber
lin
e.A
sol
uti
on o
f th
e co
mpo
un
d in
equ
alit
y is
a s
olu
tion
of
eith
er i
neq
ual
ity,
not
nec
essa
rily
bot
h.
Sol
ve 2
a�
1 �
11 o
r a
�3a
�2.
2a�
1 �
11or
a�
3a�
22a
�1
�1
�11
�1
a�
3a�
3a�
3a�
22a
�10
�2a
�2
��
a�
5a
��
1
Gra
ph a
�5.
Gra
ph a
��
1.
Fin
d th
e un
ion.
Th
e so
luti
on s
et i
s {a
a�
5}.
Gra
ph
th
e so
luti
on s
et o
f ea
ch c
omp
oun
d i
neq
ual
ity.
1.b
�2
or b
��
32.
3 �
qor
q�
13.
y�
�4
or y
�0
4.4
�p
or p
�8
5.�
3 �
dor
d�
26.
�2
�x
or 3
�x
Sol
ve e
ach
com
pou
nd
in
equ
alit
y.T
hen
gra
ph
th
e so
luti
on s
et.
7.3
�3w
or 3
w�
98.
�3p
�1
��
11 o
r p
�2
{w1
�w
}{p
p�
4 o
r p
�2}
9.2x
�4
�6
or x
�2x
�4
10.2
y�
2 �
12 o
r y
�3
�2y
{xx
�4}
{yy
�5}
11.
n�
�2
or 2
n�
2 �
6 �
n12
.3a
�2
�5
or 7
�3a
�2a
�6
{nn
is a
rea
l nu
mb
er}
{aa
��
1 o
r a
�1}
0�
1�
2�
3�
41
23
40
�1
�2
�3
�4
12
34
1 � 2
01
23
45
67
8�
2�
10
12
34
56
01
23
45
67
8�
3�
4�
2�
10
12
34
�3
�4
�2
�1
01
23
40
�1
�2
�3
�4
12
34
0�
1�
21
23
45
6
�3
�4
�5
�2
�1
01
23
�3
�4
�2
�1
01
23
4�
3�
4�
2�
10
12
34
�2
�1
01
23
45
6
�2
�1
01
23
45
6
�2
�1
01
23
45
6
2� �
2�
2a� �
210 � 2
2a � 2
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g C
om
po
un
d In
equ
alit
ies
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-4
6-4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 6-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
ract
ice
So
lvin
g C
om
po
un
d In
equ
alit
ies
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-4
6-4
©G
lenc
oe/M
cGra
w-H
ill36
3G
lenc
oe A
lgeb
ra 1
Lesson 6-4
Gra
ph
th
e so
luti
on s
et o
f ea
ch c
omp
oun
d i
neq
ual
ity.
1.b
�3
or b
�0
2.z
�3
and
z�
�2
3.k
�1
and
k�
54.
y�
�1
or y
�1
Wri
te a
com
pou
nd
in
equ
alit
y fo
r ea
ch g
rap
h.
5.6.
�3
�x
�3
1 �
x�
4
7.8.
x�
�2
or
x�
1x
��
1 o
r x
�2
Sol
ve e
ach
com
pou
nd
in
equ
alit
y.T
hen
gra
ph
th
e so
luti
on s
et.
9.m
�3
�5
and
m�
3 �
710
.y�
5 �
�4
or y
�5
�1
{m2
�m
�4}
{yy
�1
or
y�
6}
11.4
�f
�6
and
f�
6 �
512
.w�
3 �
0 or
w�
7 �
9{f
�2
�f
��
1}{w
w�
�3
or
w�
2}
13.�
6 �
b�
4 �
214
.p�
2 �
�2
or p
�2
�1
{b�
2 �
b�
6}{p
p�
0 o
r p
�3}
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.15
–17.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
15.A
nu
mbe
r pl
us
one
is g
reat
er t
han
neg
ativ
e fi
ve a
nd
less
th
an t
hre
e.�
5 �
n�
1 �
3;{n
�6
�n
�2}
16.A
nu
mbe
r de
crea
sed
by t
wo
is a
t m
ost
fou
r or
at
leas
t n
ine.
n�
2 �
4 o
r n
�2
�9;
{nn
�6
or
n�
11}
17.T
he
sum
of
a n
um
ber
and
thre
e is
no
mor
e th
an e
igh
t or
is
mor
e th
an t
wel
ve.
n�
3 �
8 o
r n
�3
�12
;{n
n�
5 o
r n
�9}�
3�
4�
2�
10
12
34
�2
�1
01
23
45
6
�3
�4
�2
�1
01
23
4�
4�
3�
2�
10
12
34
�2
�1
01
23
45
6�
2�
10
12
34
56
�4
�3
�2
�1
01
23
4�
4�
3�
2�
10
12
34
�2
�1
01
23
45
6�
2�
1�
4�
30
12
34
�3
�4
�2
�1
01
23
40
12
34
56
78
�4
�3
�2
�1
01
23
4�
3�
4�
2�
10
12
34
©G
lenc
oe/M
cGra
w-H
ill36
4G
lenc
oe A
lgeb
ra 1
Gra
ph
th
e so
luti
on s
et o
f ea
ch c
omp
oun
d i
neq
ual
ity.
1.�
4 �
e�
12.
x�
0 or
x�
3
3.g
��
3 or
g�
44.
�4
�p
�4
Wri
te a
com
pou
nd
in
equ
alit
y fo
r ea
ch g
rap
h.
5.6.
x�
�3
or
x�
3x
�2
or
x�
37.
8.
0 �
x�
5�
5 �
x�
0
Sol
ve e
ach
com
pou
nd
in
equ
alit
y.T
hen
gra
ph
th
e so
luti
on s
et.
9.k
�3
��
7 or
k�
5 �
810
.�n
�2
or 2
n�
3 �
5{k
k�
�4
or
k�
3}{n
n�
�2}
11.5
�3h
�2
�11
12.2
c�
4 �
�6
and
3c�
1 �
13{h
1 �
h�
3}{c
�1
�c
�4}
Def
ine
a va
riab
le,w
rite
an
in
equ
alit
y,an
d s
olve
eac
h p
rob
lem
.Th
en c
hec
k y
our
solu
tion
.13
–14.
Sam
ple
an
swer
:L
et n
�th
e n
um
ber
.
13.T
wo
tim
es a
nu
mbe
r pl
us
one
is g
reat
er t
han
fiv
e an
d le
ss t
han
sev
en.
5 �
2n�
1 �
7;{n
2 �
n�
3}14
.A n
um
ber
min
us
one
is a
t m
ost
nin
e,or
tw
o ti
mes
th
e n
um
ber
is a
t le
ast
twen
ty-f
our.
n�
1 �
9 o
r 2n
�24
;{n
n�
10 o
r n
�12
}
MET
EOR
OLO
GY
For
Exe
rcis
es 1
5 an
d 1
6,u
se t
he
foll
owin
g in
form
atio
n.
Str
ong
win
ds c
alle
d th
e pr
evai
lin
g w
este
rlie
s bl
ow f
rom
wes
t to
eas
t in
a b
elt
from
40°
to60
°la
titu
de i
n b
oth
th
e N
orth
ern
an
d S
outh
ern
Hem
isph
eres
.
15.W
rite
an
in
equ
alit
y to
rep
rese
nt
the
lati
tude
of
the
prev
aili
ng
wes
terl
ies.
{w4
0 �
w�
60}
16.W
rite
an
in
equ
alit
y to
rep
rese
nt
the
lati
tude
s w
her
e th
e pr
evai
lin
g w
este
rlie
s ar
e n
otlo
cate
d.{w
w�
40 o
r w
�60
}
17.N
UTR
ITIO
NA
coo
kie
cont
ains
9 g
ram
s of
fat
.If
you
eat
no f
ewer
tha
n 4
and
no m
ore
than
7 co
okie
s,ho
w m
any
gram
s of
fat
will
you
con
sum
e?b
etw
een
36
g a
nd
63
g in
clu
sive
�2
�1
01
23
45
6�
2�
1�
4�
30
12
34
�4
�3
�2
�1
01
23
4�
3�
4�
2�
10
12
34
�2
�3
�4
�5
�6
�1
01
2�
2�
10
12
34
56
�2
�1
01
23
45
6�
4�
3�
2�
10
12
34
�2
�1
�4
�3
01
23
4�
3�
4�
2�
10
12
34
0�
1�
2�
3�
41
23
4�
2�
1�
4�
3�
6�
50
12
Pra
ctic
e (
Ave
rag
e)
So
lvin
g C
om
po
un
d In
equ
alit
ies
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-4
6-4
Answers (Lesson 6-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csS
olv
ing
Co
mp
ou
nd
Ineq
ual
itie
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-4
6-4
©G
lenc
oe/M
cGra
w-H
ill36
5G
lenc
oe A
lgeb
ra 1
Lesson 6-4
Pre-
Act
ivit
yH
ow a
re c
omp
oun
d i
neq
ual
itie
s u
sed
in
tax
tab
les?
Rea
d th
e in
trod
uct
ion
to
Les
son
6-4
at
the
top
of p
age
339
in y
our
text
book
.
•E
xpla
in w
hy
it i
s po
ssib
le t
hat
Mr.
Kel
ly’s
in
com
e is
$41
,370
.
$41,
370
is g
reat
er t
han
or
equ
al t
o $
41,3
50 a
nd
less
th
an $
41,4
00.
•E
xpla
in w
hy
it i
s n
otpo
ssib
le t
hat
Mr.
Kel
ly’s
in
com
e is
$41
,400
.
$41,
400
is n
ot
less
th
an $
41,4
00.
Rea
din
g t
he
Less
on
1.W
hen
is
a co
mpo
un
d in
equ
alit
y co
nta
inin
g an
dtr
ue?
It is
tru
e w
hen
bo
th in
equ
alit
ies
are
tru
e.
2.T
he
grap
h o
f a
com
pou
nd
ineq
ual
ity
con
tain
ing
and
is t
he
of t
he
grap
hs
of t
he
two
ineq
ual
itie
s.
3.W
hen
is
a co
mpo
un
d in
equ
alit
y co
nta
inin
g or
tru
e?
It is
tru
e w
hen
on
e o
r b
oth
of
the
ineq
ual
itie
s is
tru
e.
4.T
he
grap
h o
f a
com
pou
nd
ineq
ual
ity
con
tain
ing
oris
th
e of
th
egr
aph
s of
th
e tw
o in
equ
alit
ies.
5.S
upp
ose
you
use
yel
low
to
show
th
e gr
aph
of
Ineq
ual
ity
#1 o
n t
he
nu
mbe
r li
ne.
You
use
blu
e to
sh
ow t
he
grap
h o
f In
equ
alit
y #2
.Wri
te a
nd
or o
rin
eac
h b
lan
k to
com
plet
e th
ese
nte
nce
.
a.T
he
part
th
at i
s gr
een
is
the
grap
h o
f In
equ
alit
y #1
In
equ
alit
y #2
.
b.
All
col
ored
par
ts f
orm
th
e gr
aph
of
Ineq
ual
ity
#1
Ineq
ual
ity
#2.
Hel
pin
g Y
ou
Rem
emb
er
6.O
ne
way
to
rem
embe
r so
met
hin
g is
to
con
nec
t it
to
som
eth
ing
that
is
fam
ilia
r to
you
.W
rite
tw
o tr
ue
com
pou
nd
stat
emen
ts a
bou
t yo
urs
elf,
one
usi
ng
the
wor
d an
dan
d th
eot
her
usi
ng
the
wor
d or
.
Sam
ple
an
swer
:I a
m 1
4 an
d I
am a
fre
shm
an in
hig
h s
cho
ol.
Aft
ersc
ho
ol,
I will
go
to
fo
otb
all p
ract
ice
or
I will
go
ho
me.
oran
d
un
ion
inte
rsec
tio
n
©G
lenc
oe/M
cGra
w-H
ill36
6G
lenc
oe A
lgeb
ra 1
So
me
Pro
per
ties
of
Ineq
ual
itie
sT
he
two
expr
essi
ons
on e
ith
er s
ide
of a
n i
neq
ual
ity
sym
bol
are
som
etim
es c
alle
d th
e fi
rst
and
seco
nd
mem
bers
of
the
ineq
ual
ity.
If t
he
ineq
ual
ity
sym
bols
of
two
ineq
ual
itie
s po
int
in t
he
sam
edi
rect
ion
,th
e in
equ
alit
ies
hav
e th
e sa
me
sen
se.F
or e
xam
ple,
a�
ban
d c
�d
hav
e th
e sa
me
sen
se;a
�b
and
c�
dh
ave
oppo
site
sen
ses.
In t
he
prob
lem
s on
th
is p
age,
you
wil
l ex
plor
e so
me
prop
erti
es
of i
neq
ual
itie
s.
Th
ree
of t
he
fou
r st
atem
ents
bel
ow a
re t
rue
for
all
nu
mb
ers
aan
d b
(or
a,b
,c,a
nd
d).
Wri
te e
ach
sta
tem
ent
in a
lgeb
raic
form
.If
the
stat
emen
t is
tru
e fo
r al
l n
um
ber
s,p
rove
it.
If i
t is
not
tru
e,gi
ve a
n e
xam
ple
to
show
th
at i
t is
fal
se.
1.G
iven
an
in
equ
alit
y,a
new
an
d eq
uiv
alen
t in
equ
alit
y ca
n b
ecr
eate
d by
in
terc
han
gin
g th
e m
embe
rs a
nd
reve
rsin
g th
e se
nse
.If
a�
b,t
hen
b�
a.a
�b
,a�
b�
0,�
b�
�a,
(�1)
(�b
) �
(�1)
(�a)
,b�
a
2.G
iven
an
ineq
uali
ty,a
new
and
equ
ival
ent
ineq
uali
ty c
an b
e cr
eate
dby
cha
ngin
g th
e si
gns
of b
oth
term
s an
d re
vers
ing
the
sens
e.If
a�
b,t
hen
2a
�2b
.a
�b
,a�
b�
0,�
b�
�a,
�a
��
b
3.G
iven
tw
o in
equ
alit
ies
wit
h t
he
sam
e se
nse
,th
e su
m o
f th
eco
rres
pon
din
g m
embe
rs a
re m
embe
rs o
f an
equ
ival
ent
ineq
ual
ity
wit
h t
he
sam
e se
nse
.If
a�
ban
d c
�d
,th
en a
�c
�b
�d
.a
�b
and
c �
d,s
o (
a�
b)
and
(c
�d
) ar
e p
osi
tive
nu
mb
ers,
so t
he
sum
(a
�b
) �
(c�
d)
is a
lso
po
siti
ve.
a�
b�
c�
d�
0,so
a�
c�
b�
d.
4.G
iven
tw
o in
equ
alit
ies
wit
h t
he
sam
e se
nse
,th
e di
ffer
ence
of
the
corr
espo
ndi
ng
mem
bers
are
mem
bers
of
an e
quiv
alen
t in
equ
alit
yw
ith
th
e sa
me
sen
se.
If a
�b
and
c�
d,t
hen
a�
c�
b�
d.T
he
stat
emen
t is
fal
se.5
�4
and
3 �
2,bu
t 5
�3
�4
�2.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-4
6-4
Answers (Lesson 6-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
So
lvin
g O
pen
Sen
ten
ces
Invo
lvin
g A
bso
lute
Val
ue
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-5
6-5
©G
lenc
oe/M
cGra
w-H
ill36
7G
lenc
oe A
lgeb
ra 1
Lesson 6-5
Ab
solu
te V
alu
e Eq
uat
ion
sW
hen
sol
vin
g eq
uat
ion
s th
at i
nvo
lve
abso
lute
val
ue,
ther
ear
e tw
o ca
ses
to c
onsi
der.
Cas
e 1:
Th
e va
lue
insi
de t
he
abso
lute
val
ue
sym
bols
is
posi
tive
.C
ase
2:T
he
valu
e in
side
th
e ab
solu
te v
alu
e sy
mbo
ls i
s n
egat
ive.
Sol
ve
x�
4�
1.T
hen
grap
h t
he
solu
tion
set
.
Wri
te
x�
4 �
1as
x�
4 �
1 or
x�
4 �
�1.
x�
4 �
1or
x�
4 �
�1
x�
4 �
4 �
1 �
4x
�4
��
1x
��
3x
�4
�4
��
1�4
x�
�5
Th
e so
luti
on s
et i
s {�
5,�
3}.
Th
e gr
aph
is
show
n b
elow
.
�8
�7
�6
�5
�4
�3
�2
�1
0
Wri
te a
n i
neq
ual
ity
invo
lvin
g ab
solu
te v
alu
e fo
r th
e gr
aph
.
Fin
d th
e po
int
that
is
the
sam
e di
stan
cefr
om �
2 as
it
is f
rom
4.
Th
e di
stan
ce f
rom
1 t
o �
2 is
3 u
nit
s.T
he
dist
ance
fro
m 1
to
4 is
3 u
nit
s.S
o,x
�1
�3.
10
�1
�2
�3
23
3 un
its3
units
45
�3
�2
�1
01
23
45
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Sol
ve e
ach
op
en s
ente
nce
.Th
en g
rap
h t
he
solu
tion
set
.
1.y
�
3{�
3,3}
2.x
�4
�4
{0,8
}3.
y�
3�
2{�
5,�
1}
4.b
�2
�3
{�5,
1}5.
w�
2�
5{�
3,7}
6.t
�2
�4
{�6,
2}
7.2
x�
8{�
4,4}
8.5
y�
2�
7��
1,1
�9.
p�
0.2
�0.
5{�
0.3,
0.7}
10.
d�
100
�50
{50
,150
}11.
2x
�1
�11
{�5,
6}12
. 3x�
�6
��2
,1�
For
eac
h g
rap
h,w
rite
an
op
en s
ente
nce
in
volv
ing
abso
lute
val
ue.
13.
14.
15.
x
�4
x�
1 �
2x
�3
�4
�3
�4
�5
�6
�7
�2
�1
01
�3
�4
�2
�1
01
23
40
�2
�4
�6
�8
24
68
�2
�3
�1
01
23
45
�4
�6
�2
02
46
810
5010
015
020
0
5 � 61 � 6
1 � 2
�0.
8�
0.4
00.
40.
8�
3�
4�
2�
10
12
34
�3
�4
�2
�1
01
23
4
4 � 5
�8
�6
�4
�2
02
46
8�
8�
6�
4�
20
24
68
�6
�5
�4
�3
�2
�1
01
2
�8
�7
�6
�5
�4
�3
�2
�1
00
12
34
56
78
�3
�4
�2
�1
01
23
4
©G
lenc
oe/M
cGra
w-H
ill36
8G
lenc
oe A
lgeb
ra 1
Ab
solu
te V
alu
e In
equ
alit
ies
Wh
en s
olvi
ng
ineq
ual
itie
s th
at i
nvo
lve
abso
lute
val
ue,
ther
e ar
e tw
o ca
ses
to c
onsi
der
for
ineq
ual
itie
s in
volv
ing
�(o
r �
) an
d tw
o ca
ses
to c
onsi
der
for
ineq
ual
itie
s in
volv
ing
�(o
r �
).
Rem
embe
r th
at i
neq
ual
itie
s w
ith
an
dar
e re
late
d to
in
ters
ecti
ons,
wh
ile
ineq
ual
itie
s w
ith
or
are
rela
ted
to u
nio
ns.
Sol
ve |
3a�
4| �
10.T
hen
gra
ph
th
e so
luti
on s
et.
Wri
te
3a�
4�
10 a
s 3a
�4
�10
an
d 3a
�4
��
10.
3a�
4 �
10an
d3a
�4
��
103a
�4
�4
�10
�4
3a�
4 �
4 �
�10
�4
3a�
63a
��
14
��
a�
2a
��
4
Th
e so
luti
on s
et i
s �a
�4
�a
�2 �.
Sol
ve e
ach
op
en s
ente
nce
.Th
en g
rap
h t
he
solu
tion
set
.
1.c
�2
�6
2.x
�9
�0
3.3
f�
10
�4
{cc
��
4 o
r c
�8}
��f
�4
�f
��
2 �
4.x
�
25.
x
�3
6.2
x�
1�
�2
{x�
2 �
x�
2}{x
x�
�3
or
x�
3}{x
xis
a r
eal n
um
ber
}
7.2
d�
1�
48.
3 �
(x�
1)
�8
9.3
r�
2�
�5
�d �
1�
d�
2�
{x�
4 �
x�
12}
�
For
eac
h g
rap
h,w
rite
an
op
en s
ente
nce
in
volv
ing
abso
lute
val
ue.
10.
11.
12.
x
�1
x�
2 �
1x
�1
�3
�2
�1
�3
01
23
45
�4
�3
�2
�1
01
23
4�
4�
3�
2�
10
12
34
�4
�3
�2
�1
01
23
4�
4�
20
24
68
1012
�4
�3
�2
�1
01
23
4
1 � 21 � 2
0�
1�
2�
3�
41
23
40
�1
�2
�3
�4
12
34
�4
�3
�2
�1
01
23
4
�6
�5
�4
�3
�2
�1
01
2�
4�
3�
2�
10
12
34
20
�2
�4
�6
46
810
2 � 3
2 � 3
2 � 3
�14
�3
3a � 36 � 3
3a � 3
If x
�
n, t
hen
x�
�n
and
x�
n.If
x
�n,
the
n x
�n
or x
��
n.
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
So
lvin
g O
pen
Sen
ten
ces
Invo
lvin
g A
bso
lute
Val
ue
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-5
6-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Now
gra
ph t
he
solu
tion
set
.
�2
�1
�4
�5
�3
01
23
Answers (Lesson 6-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
So
lvin
g O
pen
Sen
ten
ces
Invo
lvin
g A
bso
lute
Val
ue
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-5
6-5
©G
lenc
oe/M
cGra
w-H
ill36
9G
lenc
oe A
lgeb
ra 1
Lesson 6-5
Mat
ch e
ach
op
en s
ente
nce
wit
h t
he
grap
h o
f it
s so
luti
on s
et.
1.x
�
2c
a.
2.x
�5
�3
ab
.
3.x
�2
�3
dc.
4.x
�1
�4
bd
.
Exp
ress
eac
h s
tate
men
t u
sin
g an
in
equ
alit
y in
volv
ing
abso
lute
val
ue.
Do
not
solv
e.
5.T
he
wea
ther
man
pre
dict
ed t
hat
th
e te
mpe
ratu
re w
ould
be
wit
hin
3°
of 5
2°F.
t�
52
�3
6.S
eren
a w
ill
mak
e th
e B
tea
m i
f sh
e sc
ores
wit
hin
8 p
oin
ts o
f th
e te
am a
vera
ge o
f 92
.
p�
92
�8
7.T
he
dan
ce c
omm
itte
e ex
pect
s at
ten
dan
ce t
o n
um
ber
wit
hin
25
of l
ast
year
’s 8
7 st
ude
nts
.
a�
87
�25
Sol
ve e
ach
op
en s
ente
nce
.Th
en g
rap
h t
he
solu
tion
set
.
8.s
�1
�5
{�6,
4}9.
c�
3�
1{c
2 �
c�
4}
10.
n�
2�
1{n
n�
�3
or
n�
�1}
11.
t�
6�
4{t
t�
�10
or
t�
�2}
12.
w�
2�
2{0
,4}
13.
k�
5�
4{k
1 �
k�
9}
For
eac
h g
rap
h,w
rite
an
op
en s
ente
nce
in
volv
ing
abso
lute
val
ue.
14.
15.
x
�1
x�
3 �
2
16.
17.
x�
4 �
1x
�
4
�2
�3
�4
�5
�1
01
23
45
�2
�3
�4
�5
�1
01
23
45
�2
�3
�4
�5
�6
�7
�1
01
23
�5
�4
�3
�2
�1
01
23
45
01
23
45
67
89
10�
3�
4�
2�
10
12
34
56
�8
�7
�10
�9
�6
�5
�4
�3
�2
�1
0�
2�
1�
4�
5�
6�
30
12
34
�3
�1
01
23
45
6�
27
�3
�4
�5
�6
�2
�1
01
23
4
�2
�3
�4
�1
01
23
45
6
�2
�3
�4
�5
�1
01
23
45
�2
�3
�4
�5
�1
01
23
45
�8
�9
�10
�7
�6
�5
�4
�3
�2
�1
0
©G
lenc
oe/M
cGra
w-H
ill37
0G
lenc
oe A
lgeb
ra 1
Mat
ch e
ach
op
en s
ente
nce
wit
h t
he
grap
h o
f it
s so
luti
on s
et.
1.x
�7
�3
ca.
2.x
�3
�1
ab
.
3.2
x�
1�
5d
c.
4.5
�x
�3
bd
.
Exp
ress
eac
h s
tate
men
t u
sin
g an
in
equ
alit
y in
volv
ing
abso
lute
val
ue.
Do
not
solv
e.
5.T
he
hei
ght
of t
he
plan
t m
ust
be
wit
hin
2 i
nch
es o
f th
e st
anda
rd 1
3-in
ch s
how
siz
e.h
�13
�
2
6.T
he
maj
orit
y of
gra
des
in S
ean
’s E
ngl
ish
cla
ss a
re w
ith
in 4
poi
nts
of
85.
g�
85
�4
Sol
ve e
ach
op
en s
ente
nce
.Th
en g
rap
h t
he
solu
tion
set
.
7.|2
z�
9| �
1{z
4
�z
�5}
8.|3
�2r
| �
7{r
r
��
2 o
r r
�5}
9.|3
t�
6| �
9{t
�
5 �
t�
1}10
.|2g
�5|
�9
{gg
��
2 o
r g
�7}
For
eac
h g
rap
h,w
rite
an
op
en s
ente
nce
in
volv
ing
abso
lute
val
ue.
11.
12.
x�
6 �
5x
�4
�2
13.
14.
x�
3 �
4x
�2
�4
15.F
ITN
ESS
Tai
sha
use
s th
e el
lipt
ical
cro
ss-t
rain
er a
t th
e gy
m.H
er g
ener
al g
oal
is t
o bu
rn28
0 C
alor
ies
per
wor
kou
t,bu
t sh
e va
ries
by
as m
uch
as
25 C
alor
ies
from
th
is a
mou
nt
onan
y gi
ven
day
.Wh
at i
s th
e ra
nge
of
the
nu
mbe
r of
Cal
orie
s bu
rned
for
Tai
sha’
s cr
oss-
trai
ner
wor
kou
t?{c
255
�c
�30
5}
16.T
EMPE
RA
TUR
EA
th
erm
omet
er i
s gu
aran
teed
to
give
a t
empe
ratu
re n
o m
ore
than
1.2°
F f
rom
th
e ac
tual
tem
pera
ture
.If
the
ther
mom
eter
rea
ds 2
8°F,
wh
at i
s th
e ra
nge
for
the
actu
al t
empe
ratu
re?
{t2
6.8
�t
�29
.2}
�2
�3
�1
01
23
45
67
�2
�3
�4
�5
�6
�7
�8
�1
01
2
�2
�3
�4
�5
�6
�7
�8
�1
01
21
23
45
67
89
1011
�2
�1
01
23
45
67
8�
5�
4�
3�
2�
10
12
34
5
�5
�4
�3
�2
�1
01
23
45
�5
�4
�3
�2
�1
01
23
45
�2
�3
�4
�5
�1
01
23
45
�8
�9
�10
�7
�6
�5
�4
�3
�2
�1
0
�2
�1
01
23
45
67
8
�2
�3
�4
�5
�1
01
23
45
Pra
ctic
e (
Ave
rag
e)
So
lvin
g O
pen
Sen
ten
ces
Invo
lvin
g A
bso
lute
Val
ue
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-5
6-5
Answers (Lesson 6-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
olv
ing
Op
en S
ente
nce
s In
volv
ing
Ab
solu
te V
alu
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-5
6-5
©G
lenc
oe/M
cGra
w-H
ill37
1G
lenc
oe A
lgeb
ra 1
Lesson 6-5
Pre-
Act
ivit
yH
ow i
s ab
solu
te v
alu
e u
sed
in
ele
ctio
n p
olls
?
Rea
d th
e in
trod
uct
ion
to
Les
son
6-5
at
the
top
of p
age
345
in y
our
text
book
.
•W
hat
doe
s th
e ph
rase
mar
gin
of
erro
r m
ean
to
you
?
Sam
ple
an
swer
:Th
e n
um
ber
of
po
ints
a r
epo
rted
res
ult
may
be
off
fro
m t
he
exac
t re
sult
.
•In
th
is p
oll,
the
nu
mbe
r of
peo
ple
oppo
sed
to t
he
tax
levy
may
be
as
hig
h a
s or
as
low
as
.Th
is c
an b
e w
ritt
en a
s
the
ineq
ual
ity
x�
�
3.
Rea
din
g t
he
Less
on
Com
ple
te e
ach
com
pou
nd
sen
ten
ce b
y w
riti
ng
an
dor
or
in t
he
bla
nk
.Use
th
ere
sult
to
hel
p y
ou g
rap
h t
he
abso
lute
val
ue
sen
ten
ce.
Ab
solu
te V
alu
eS
ente
nce
Co
mp
ou
nd
Sen
ten
ceG
rap
h
1.2
x�
2�
82x
�2
�8
2x�
2 �
�8
2.x
�5
�4
x�
5 �
4 x
�5
��
4
3.2
x�
3�
52x
�3
�5
2x�
3 �
�5
4.H
ow w
ould
you
wri
te t
he
com
pou
nd
sen
ten
ce 3
x�
7 �
5 or
3x
�7
��
5 as
an
abs
olu
teva
lue
sen
ten
ce?
3x
�7
�5
Hel
pin
g Y
ou
Rem
emb
er
5.R
ecal
l th
at
xte
lls
you
how
man
y u
nit
s th
e n
um
ber
xis
fro
m z
ero
on t
he
nu
mbe
r li
ne.
Exp
lain
th
e m
ean
ing
of
x�
n,
x�
n,a
nd
x
�n
by u
sin
g th
e id
ea o
f th
e di
stan
cefr
om x
to z
ero.
x
�n
mea
ns
xis
exa
ctly
nu
nit
s fr
om
zer
o.
x�
nm
ean
s x
is le
ss
than
nu
nit
s fr
om
zer
o.
x�
nm
ean
s x
is m
ore
th
an n
un
its
fro
m z
ero
.
�2
�3
�1
01
23
45
67
or
01
23
45
67
89
10an
d
�3
�4
�5
�6
�2
�1
01
23
4o
r
4542
%48
%
©G
lenc
oe/M
cGra
w-H
ill37
2G
lenc
oe A
lgeb
ra 1
Pre
cisi
on
of
Mea
sure
men
tT
he
prec
isio
n o
f a
mea
sure
men
t de
pen
ds b
oth
on
you
r ac
cura
cy i
nm
easu
rin
g an
d th
e n
um
ber
of d
ivis
ion
s on
th
e ru
ler
you
use
.Su
ppos
eyo
u m
easu
red
a le
ngt
h o
f w
ood
to t
he
nea
rest
on
e-ei
ghth
of
an i
nch
an
d go
t a
len
gth
of
6in
.
Th
e dr
awin
g sh
ows
that
th
e ac
tual
mea
sure
men
t li
es s
omew
her
e
betw
een
6in
.an
d 6
in.T
his
mea
sure
men
t ca
n b
e w
ritt
en u
sin
g
the
sym
bol
�,w
hic
h i
s re
ad p
lus
or m
inu
s.It
can
als
o be
wri
tten
as
aco
mpo
un
d in
equ
alit
y.
6�
in.
6in
.�m
�6
in.
In t
his
exa
mpl
e,in
.is
the
abso
lute
err
or.T
he
abso
lute
err
or i
s
one-
hal
f th
e sm
alle
st u
nit
use
d in
a m
easu
rem
ent.
Wri
te e
ach
mea
sure
men
t as
a c
omp
oun
d i
neq
ual
ity.
Use
th
e va
riab
le m
.
1.3
�in
.2.
9.78
�0.
005
cm3.
2.4
�0.
05 g
3in
.�m
�3
in.
9.77
5 cm
�m
�2.
35 g
�m
�2.
45 g
9.78
5 cm
4.28
�ft
5.15
�0.
5 cm
6.�
in.
27ft
�m
�28
ft14
.5 c
m �
m�
in.�
m�
in.
15.5
cm
For
eac
h m
easu
rem
ent,
give
th
e sm
alle
st u
nit
use
d a
nd
th
e ab
solu
te e
rror
.
7.12
.5 c
m �
m�
13.5
cm
8.12
in.�
m�
12in
.
1 cm
,0.5
cm
in.,
in.
9.56
in.�
m�
57in
.10
.23.
05 m
m �
m�
23.1
5 m
m
1 in
.,in
.0.
1 m
m,0
.05
mm
1 � 2
1 � 21 � 2
1 � 81 � 4
3 � 81 � 8
45 � 6443 � 64
1 � 21 � 2
1 � 6411 � 16
1 � 2
3 � 41 � 4
1 � 41 � 2
1 � 16
11 � 169 � 16
1 � 165 � 8
11 � 169 � 11
56
78
65 – 8
5 � 8
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-5
6-5
Answers (Lesson 6-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Gra
ph
ing
Ineq
ual
itie
s in
Tw
o V
aria
bles
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-6
6-6
©G
lenc
oe/M
cGra
w-H
ill37
3G
lenc
oe A
lgeb
ra 1
Lesson 6-6
Gra
ph
Lin
ear
Ineq
ual
itie
sT
he
solu
tion
set
of
an i
neq
ual
ity
that
in
volv
es t
wo
vari
able
s is
gra
phed
by
grap
hin
g a
rela
ted
lin
ear
equ
atio
n t
hat
for
ms
a bo
un
dary
of
a h
alf-
pla
ne.
Th
e gr
aph
of
the
orde
red
pair
s th
at m
ake
up
the
solu
tion
set
of
the
ineq
ual
ity
fill
a r
egio
n o
f th
e co
ordi
nat
e pl
ane
on o
ne
side
of
the
hal
f-pl
ane.
Gra
ph
y�
�3x
�2.
Gra
ph y
��
3x�
2.S
ince
y�
�3x
�2
is t
he
sam
e as
y�
�3x
�2
and
y�
�3x
�2,
the
bou
nda
ry i
s in
clu
ded
in t
he
solu
tion
set
an
d th
e gr
aph
sh
ould
be
draw
n a
s a
soli
d li
ne.
Sel
ect
a po
int
in e
ach
hal
f pl
ane
and
test
it.
Ch
oose
(0,
0) a
nd
(�2,
�2)
.
y�
�3x
�2
y�
�3x
�2
0 �
�3(
0) �
2�
2 �
�3(
�2)
�2
0 �
�2
is f
alse
.�
2 �
6 �
2�
2 �
4 is
tru
e.T
he
hal
f-pl
ane
that
con
tain
s (�
2,�
2) c
onta
ins
the
solu
tion
.Sh
ade
that
hal
f-pl
ane.
Gra
ph
eac
h i
neq
ual
ity.
1.y
�4
2.x
�1
3.3x
�y
4.�
x�
y5.
x�
y�
16.
2x�
3y�
6
7.y
��
x�
38.
4x�
3y�
69.
3x�
6y�
12
x
y
O
x
y
O
x
y
O
1 � 2
x
y
Ox
y
Ox
y
O
x
y
Ox
y
O
x
y
O
x
y O
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill37
4G
lenc
oe A
lgeb
ra 1
Solv
e R
eal-
Wo
rld
Pro
ble
ms
Wh
en s
olvi
ng
real
-lif
e in
equ
alit
ies,
the
dom
ain
an
dra
nge
of
the
ineq
ual
ity
are
ofte
n r
estr
icte
d to
non
neg
ativ
e n
um
bers
or
to w
hol
e n
um
bers
.
BA
NK
ING
A b
ank
off
ers
4.5%
an
nu
al i
nte
rest
on
reg
ula
r sa
vin
gsac
cou
nts
an
d 6
% a
nn
ual
in
tere
st o
n c
erti
fica
tes
of d
epos
it (
CD
).If
Mar
jean
wan
tsto
ear
n a
t le
ast
$300
in
tere
st p
er y
ear,
how
mu
ch m
oney
sh
ould
sh
e d
epos
it i
nea
ch t
ype
of a
ccou
nt?
Let
x�
the
amou
nt
depo
site
d in
a r
egu
lar
savi
ngs
acc
oun
t.L
et y
�th
e am
oun
t de
posi
ted
in a
CD
.T
hen
0.0
45x
�0.
06y
�30
0 is
an
ope
n s
ente
nce
re
pres
enti
ng
this
sit
uat
ion
.
Sol
ve f
or y
in t
erm
s of
x.
0.04
5x�
0.06
y�
300
Orig
inal
ineq
ualit
y
0.06
y�
�0.
045x
�30
0S
ubtr
act
0.04
5xfr
om e
ach
side
.
y�
�0.
75x
�50
00D
ivid
e ea
ch s
ide
by 0
.06.
Gra
ph y
��
0.75
x�
5000
an
d te
st t
he
poin
t (0
,0).
Sin
ce 0
��
0.75
(0)
�50
00 i
s fa
lse,
shad
e th
e h
alf-
plan
e th
at d
oes
not
con
tain
(0,
0).
On
e so
luti
on i
s (4
000,
2000
).T
his
rep
rese
nts
$40
00
depo
site
d at
4.5
% a
nd
$2,0
00 d
epos
ited
at
6%.
1.SO
CIA
L EV
ENTS
Tic
kets
for
th
e sc
hoo
l pl
ay c
ost
$5 p
er
stu
den
t an
d $7
per
adu
lt.T
he
sch
ool
wan
ts t
o ea
rn a
t le
ast
$5,4
00 o
n e
ach
per
form
ance
.
a.W
rite
an
in
equ
alit
y th
at r
epre
sen
ts t
his
sit
uat
ion
.5x
�7y
�54
00
b.G
raph
th
e so
luti
on s
et.
c.If
500
adu
lt t
icke
ts a
re s
old,
wh
at i
s th
e m
inim
um
nu
mbe
r of
stu
den
t ti
cket
s th
at m
ust
be
sold
?38
0
2.M
AN
UFA
CTU
RIN
GA
n a
uto
par
ts c
ompa
ny
can
pro
duce
525
fou
r-cy
lin
der
engi
nes
or
270
V-6
en
gin
es p
er d
ay.I
t w
ants
to
prod
uce
up
to 3
00,0
00 e
ngi
nes
per
yea
r.
a.W
rite
an
in
equ
alit
y th
at r
epre
sen
ts t
his
sit
uat
ion
.52
5f�
270s
�30
0000
b.A
re t
her
e re
stri
ctio
ns
on t
he
dom
ain
or
ran
ge?
Nei
ther
fn
or
sis
neg
ativ
e.
3.G
EOM
ETRY
Th
e pe
rim
eter
of
a re
ctan
gula
r lo
t is
les
s th
an 8
00 f
eet.
Wri
te a
nin
equ
alit
y th
at r
epre
sen
ts t
he
amou
nt
of f
enci
ng
that
wil
l en
clos
e th
e lo
t.2�
�2w
�80
0
Tick
et
Sale
s
Stu
den
t Ti
cket
s
Adult Tickets
300
060
090
0x
y
900
600
300
Inte
rest
on
Acc
ou
nts
Reg
ula
r Sa
vin
gs
Acc
ou
nt
($)
CD Account ($)
2000
040
0060
00x
y
6000
4000
2000
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Gra
ph
ing
Ineq
ual
itie
s in
Tw
o V
aria
bles
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-6
6-6
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 6-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
ract
ice
Gra
ph
ing
Ineq
ual
itie
s in
Tw
o V
aria
bles
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-6
6-6
©G
lenc
oe/M
cGra
w-H
ill37
5G
lenc
oe A
lgeb
ra 1
Lesson 6-6
Det
erm
ine
wh
ich
ord
ered
pai
rs a
re p
art
of t
he
solu
tion
set
for
eac
h i
neq
ual
ity.
1.y
�3x
,{(1
,5),
(1,0
),(�
1,0)
,(5,
1)}
{(1,
5),(
�1,
0)}
2.y
�x
�3,
{(2,
�3)
,(�
2,�
1),(
1,6)
,(3,
4)}
{(1,
6)}
3.y
�x
�1,
{(3,
1),(
�2,
�4)
,(4,
�2)
,(�
3,3)
}{(
3,1)
,(�
2,�
4),(
4,�
2)}
Mat
ch e
ach
in
equ
alit
y w
ith
its
gra
ph
.
4.y
�2x
�2
ba.
b.
5.y
��
3xd
6.2y
�x
�4
a
7.x
�y
�1
cc.
d.
Gra
ph
eac
h i
neq
ual
ity.
8.y
��
19.
y�
x�
510
.y�
3x
11.y
�2x
�4
12.y
�x
�3
13.y
�x
�1
x
y
Ox
y
Ox
y
O
x
y
O
x
y
O
x
y
O
x
y
Ox
y
O
x
y O
x
y
O
©G
lenc
oe/M
cGra
w-H
ill37
6G
lenc
oe A
lgeb
ra 1
Det
erm
ine
wh
ich
ord
ered
pai
rs a
re p
art
of t
he
solu
tion
set
for
eac
h i
neq
ual
ity.
1.3x
�y
�6,
{(4,
3),(
�2,
4),(
�5,
�3)
,(3,
�3)
}{(
4,3)
,(3,
�3)
}
2.y
�x
�3,
{(6,
3),(
�3,
2),(
3,�
2),(
4,3)
}{(
�3,
2)}
3.3x
�2y
�5,
{(4,
�4)
,(3,
5),(
5,2)
,(�
3,4)
}{(
3,5)
,(�
3,4)
}
Mat
ch e
ach
in
equ
alit
y w
ith
its
gra
ph
.
4.5y
�2x
�10
da.
b.
5.3y
�3x
�9
c
6.y
�2x
�3
b
7.x
�2y
��
6a
c.d
.
Gra
ph
eac
h i
neq
ual
ity.
8.2y
�x
��
49.
2x�
2y�
810
.3y
�2x
�3
11. M
OV
ING
A m
ovin
g va
n h
as a
n i
nte
rior
hei
ght
of 7
fee
t (8
4 in
ches
).Yo
u h
ave
boxe
s in
12 i
nch
an
d 15
in
ch h
eigh
ts,a
nd
wan
t to
sta
ck t
hem
as
hig
h a
s po
ssib
le t
o fi
t.W
rite
an
ineq
ual
ity
that
rep
rese
nts
th
is s
itu
atio
n.
12x
�15
y�
84
BU
DG
ETIN
GF
or E
xerc
ises
12
and
13,
use
th
e fo
llow
ing
info
rmat
ion
.
Sat
chi
fou
nd
a u
sed
book
stor
e th
at s
ells
pre
-ow
ned
vid
eos
and
CD
s.V
ideo
s co
st $
9 ea
ch,a
nd
CD
s co
st $
7 ea
ch.S
atch
i ca
n s
pen
d n
o m
ore
than
$35
.
12.W
rite
an
in
equ
alit
y th
at r
epre
sen
ts t
his
sit
uat
ion
.9x
�7y
�35
13.D
oes
Sat
chi
hav
e en
ough
mon
ey t
o bu
y 2
vide
os a
nd
3 C
Ds?
No
,th
e p
urc
has
es w
ill b
e $3
9,w
hic
h is
gre
ater
th
an $
35.
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y O
x
y
O
Pra
ctic
e (
Ave
rag
e)
Gra
ph
ing
Ineq
ual
itie
s in
Tw
o V
aria
bles
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-6
6-6
Answers (Lesson 6-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csG
rap
hin
g In
equ
alit
ies
in T
wo
Var
iabl
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-6
6-6
©G
lenc
oe/M
cGra
w-H
ill37
7G
lenc
oe A
lgeb
ra 1
Lesson 6-6
Pre-
Act
ivit
yH
ow a
re i
neq
ual
itie
s u
sed
in
bu
dge
ts?
Rea
d th
e in
trod
uct
ion
to
Les
son
6-6
at
the
top
of p
age
352
in y
our
text
book
.
Wh
at d
o 3
and
4 re
pres
ent
in t
he
term
s 3x
and
4y?
the
aver
age
amo
un
t sp
ent
on
a c
afet
eria
lun
ch a
nd
a
fast
-fo
od
lun
ch
Rea
din
g t
he
Less
on
1.C
ompl
ete
the
char
t to
sh
ow w
hic
h t
ype
of l
ine
is n
eede
d fo
r ea
ch s
ymbo
l.
Sym
bo
lTy
pe
of
Lin
eB
ou
nd
ary
Par
t o
f S
olu
tio
n?
�d
ash
edn
o
�d
ash
edn
o
�so
lidye
s
�so
lidye
s
2.If
a t
est
poin
t re
sult
s in
a f
alse
sta
tem
ent,
wh
at d
o yo
u k
now
abo
ut
the
grap
h?
Th
e h
alf-
pla
ne
con
tain
ing
th
e te
st p
oin
t is
no
t p
art
of
the
solu
tio
n a
nd
is
no
t sh
aded
.
3.If
a t
est
poin
t re
sult
s in
a t
rue
stat
emen
t,w
hat
do
you
kn
ow a
bou
t th
e gr
aph
?
Th
e h
alf-
pla
ne
con
tain
ing
th
e te
st p
oin
t is
par
t o
f th
e so
luti
on
an
d
is s
had
ed.
4.W
hen
can
th
e or
igin
not
be u
sed
as a
tes
t po
int?
Th
e o
rig
in c
ann
ot
be
use
d a
s a
test
po
int
wh
en it
is o
n t
he
bo
un
dar
y.
Hel
pin
g Y
ou
Rem
emb
er
5.T
he
two-
vari
able
in
equ
alit
ies
in t
his
les
son
can
be
solv
ed f
or y
in t
erm
s of
xto
get
ase
nte
nce
in
slo
pe-i
nte
rcep
t fo
rm.I
t lo
oks
mu
ch l
ike
a sl
ope-
inte
rcep
t eq
uat
ion
,bu
t it
has
an i
neq
ual
ity
sym
bol
inst
ead
of a
n e
qual
s si
gn.F
or e
xam
ple,
4x�
2y�
5 ca
n b
e w
ritt
en
as y
��
2x�
.Exp
lain
how
to
grap
h a
n i
neq
ual
ity
once
it
is w
ritt
en i
n s
lope
-in
terc
ept
form
.Use
th
e id
ea t
hat
gre
ater
can
mea
n a
bove
and
less
can
mea
n b
elow
.
Dra
w t
he
bo
un
dar
y lin
e.If
th
e in
equ
alit
y sy
mb
ol i
s �
or
�,m
ake
the
bo
un
dar
y d
ash
ed.I
f th
e sy
mb
ol i
s �
or
�,m
ake
the
bo
un
dar
y lin
e so
lid.
If t
he
sym
bo
l in
th
e sl
op
e-in
terc
ept
ineq
ual
ity
is �
or
�,s
had
e b
elo
w t
he
bo
un
dar
y to
ind
icat
e sm
alle
r va
lues
of
y.If
th
e sy
mb
ol i
s �
or
�,s
had
eab
ove
the
bo
un
dar
y to
ind
icat
e g
reat
er v
alu
es o
f y.
5 � 2
©G
lenc
oe/M
cGra
w-H
ill37
8G
lenc
oe A
lgeb
ra 1
Usi
ng
Eq
uat
ion
s:Id
eal W
eig
ht
You
can
fin
d yo
ur
idea
l w
eigh
t as
fol
low
s.
A w
oman
sh
ould
wei
gh 1
00 p
oun
ds f
or t
he
firs
t 5
feet
of
hei
ght
and
5 ad
diti
onal
pou
nds
for
eac
h i
nch
ove
r 5
feet
(5
feet
�60
in
ches
).A
man
sh
ould
wei
gh 1
06 p
oun
ds f
or t
he
firs
t 5
feet
of
hei
ght
and
6 ad
diti
onal
pou
nds
for
eac
h i
nch
ove
r 5
feet
.Th
ese
form
ula
s ap
ply
tope
ople
wit
h n
orm
al b
one
stru
ctu
res.
To
dete
rmin
e yo
ur
bon
e st
ruct
ure
,wra
p yo
ur
thu
mb
and
inde
x fi
nge
rar
ound
the
wri
st o
f yo
ur o
ther
han
d.If
the
thu
mb
and
fing
er ju
st t
ouch
,yo
u h
ave
nor
mal
bon
e st
ruct
ure
.If
they
ove
rlap
,you
are
sm
all-
bon
ed.
If t
hey
don
’t ov
erla
p,yo
u a
re l
arge
-bon
ed.S
mal
l-bo
ned
peo
ple
shou
ldde
crea
se t
hei
r ca
lcu
late
d id
eal
wei
ght
by 1
0%.L
arge
-bon
ed p
eopl
esh
ould
in
crea
se t
he
valu
e by
10%
.
Cal
cula
te t
he
idea
l w
eigh
ts o
f th
ese
peo
ple
.
1.w
oman
,5 f
t 4
in.,
nor
mal
-bon
ed2.
man
,5 f
t 11
in
.,la
rge-
bon
ed12
0 lb
189.
2 lb
3.m
an,6
ft
5 in
.,sm
all-
bon
ed4.
you
,if
you
are
at
leas
t 5
ft t
all
187.
2 lb
An
swer
s w
ill v
ary.
For
Exe
rcis
es 5
–9,u
se t
he
foll
owin
g in
form
atio
n.
Su
ppos
e a
nor
mal
-bon
ed m
an i
s x
inch
es t
all.
If h
e is
at
leas
t 5
feet
tall
,th
en x
�60
rep
rese
nts
th
e n
um
ber
of i
nch
es t
his
man
is
over
5
feet
tal
l.F
or e
ach
of
thes
e in
ches
,his
ide
al w
eigh
t is
in
crea
sed
by
6 po
un
ds.T
hu
s,h
is p
rope
r w
eigh
t (y
) is
giv
en b
y th
e fo
rmu
la
y�
6(x
�60
) �
106
or y
�6x
�25
4.If
th
e m
an i
s la
rge-
bon
ed,t
he
form
ula
bec
omes
y�
6x�
254
�0.
10(6
x�
254)
.
5.W
rite
th
e fo
rmu
la f
or t
he
wei
ght
of a
lar
ge-b
oned
man
in
slo
pe-
inte
rcep
t fo
rm.
y�
6.6x
�27
9.4
6.D
eriv
e th
e fo
rmu
la f
or t
he
idea
l w
eigh
t (y
) of
a n
orm
al-b
oned
fem
ale
wit
h h
eigh
t x
inch
es.W
rite
th
e fo
rmu
la i
n
slop
e-in
terc
ept
form
.y
�5x
�20
0
7.D
eriv
e th
e fo
rmu
la i
n s
lope
-in
terc
ept
form
for
th
e id
eal
wei
ght
(y)
of a
lar
ge-b
oned
fem
ale
wit
h h
eigh
t x
inch
es.
y�
5.5x
�22
0
8.D
eriv
e th
e fo
rmu
la i
n s
lope
-in
terc
ept
form
for
th
e id
eal
wei
ght
(y)
of a
sm
all-
bon
ed m
ale
wit
h h
eigh
t x
inch
es.
y�
5.4x
�22
8.6
9.F
ind
the
hei
ghts
at
wh
ich
nor
mal
-bon
ed m
ales
an
d la
rge-
bon
edfe
mal
es w
ould
wei
gh t
he
sam
e.68
in.,
or
5 ft
8 in
.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
6-6
6-6
Answers (Lesson 6-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. B
D
B
B
A
D
D
A
B
A
C
�1
B
B
D
A
C
D
A
D
B
C
B
D
D
A
D
B
D
B
C
A
Chapter 6 Assessment Answer Key Form 1 Form 2APage 379 Page 380 Page 381
(continued on the next page)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: {x ��3 � x � 4}
A
B
B
C
B
D
C
A
D
B
B
C
B
A
D
D
D
B
A
A
{�12, 12}
D
D
A
A
C
C
C
A
D
Chapter 6 Assessment Answer KeyForm 2A (continued) Form 2BPage 382 Page 383 Page 384
An
swer
s
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:�3 1 117
y
xO
(0, �4)
(3, �2)
y
xO
�w ��3 � w � 2�13
��{�2, 1.5}
�1�2�3�4 0 1 2 43
{x �x � 1 or x � 2}
�1�2�3�4 0 1 2 43
{�1, 3}
�1�2�3�4 0 1 2 43
�2 0 2 4 86
{b ��2 � b � 7}0
{x �x is a real number}
�1�2�3�4�5�6 0 1 2
{w ��5 � w � 2}
{c �c � 13}
{p �p � 2}
{x �x � 8}
{a �a � 9}
{r �r � �5.5}
{y �y � �5.5}
{t �t � 84}
�b�b � �1�35
��
{z �z � �4}
{t �t � 6}
�17�19�21 �15
{n�n � �19}131211109 14 15 1716
{x �x � 13}
Chapter 6 Assessment Answer KeyForm 2CPage 385 Page 386
Sample answer:n � the number;2 n � 7; {n�n � 5}
Sample answer:n � the number of checks;3.5 � 2.5 0.1n � 5;Between 10 and 25 checks.
3x 0.75y � 20;No, the costwould be morethan $20.00.
© Glencoe/McGraw-Hill A23 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B:�7 �5 3 5
y
xO
y
xO
(0, 0)
(1, 3)
�c � c � ��13
� or c � 3�
{1, 4}
�1�2�3 0 1 2 4 53
{w ��3 � w � 5}�11 30
{�11, 3}
�1�2�3�4 0 1 2 43
{x �x � 2}�1�2 0 1 2 4 5 63
{y � 0.5 � y � 4}0
{w � w is a real number.}
�1�2�3�4 0 1 2 43
{w � 2 � w � 3}
{x � x � �11}
{w � w � �5}
{t � t � �5.5}
{f � f � 0.25}
{m � m � 6}
{k � k � 3.5}
�z � z � �3�13
��{h � h � 27}
{k �k � 5}
{s�s � 9}
�7�9�11 �5
{m�m � �9}1312111098 14 15 16
{y �y � 12}
Chapter 6 Assessment Answer KeyForm 2DPage 387 Page 388
An
swer
s
Sample answer:n � the number ofchecks;5.75 � 3.75 0.1n � 7.25;Between 20 and 35 checks.
28x 4y � 75;No, the costwould be morethan $75.00.
Sample answer:n � the number;14 � n 5; {n � n � 9}
© Glencoe/McGraw-Hill A24 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
16x 12y � 120; 3
y
xO
(0, 0)
(1, �3)
�1�2 0 1 2 4 5 63
{x �x � �1 or x � 4}
�1�2 0 1 2 4 5 63
{x ��2 � x � 6}
�2.8 40
{�2.8, 4}
�6 80
{x ��6 � x � 8}
�1�2�3�4�5�6�7�8�9
{n�n � �6}
0
{x � x � �9}
{b � b � 0.5}
�t � t � �191��
{w � w � �10.4}
3635343332 37 38 4039
{t � t � 36}
9.3
{m�m � 9.3}
Chapter 6 Assessment Answer KeyForm 3Page 389 Page 390
Sample answer:n � the number;n � 15 � 2n 8;{n � n � �23}
Sample answer:n � the number;
��37
� n � 2;
�n � n � 2�37
��
Sample answer:j � cost of jeans;2(19.89) j � 78;no more than $38.22Sample answer:n � small positiveeven integer;n n 2 � 15;6, 8; 4, 6; 2, 4
Sample answer:s � amount of sales;32,500 � 0.1s 25,600 �41,900 between $69,000and $163,000
false; Sample answer:x � 3 and y � 1.If xy � 0, x and ycannot both bepositive so x � 3 andy � 1 is false.
Chapter 6 Assessment Answer KeyPage 391, Open-Ended Assessment
Scoring Rubric
© Glencoe/McGraw-Hill A25 Glencoe Algebra 1
Score General Description Specific Criteria
• Shows thorough understanding of the concepts of usingthe properties of inequalities, solving inequalities, solvingcompound inequalities, solving open sentences involvingabsolute value, and graphing inequalities in two variables.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs are accurate and appropriate.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts of using theproperties of inequalities, solving inequalities, solvingcompound inequalities, solving open sentences involvingabsolute value, and graphing inequalities in two variables.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs are mostly accurate and appropriate.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts of usingthe properties of inequalities, solving inequalities, solvingcompound inequalities, solving open sentences involvingabsolute value, and graphing inequalities in two variables.
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs are mostly accurate.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work is shown to substantiate
the final computation.• Graphs may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of most of the concepts ofusing the properties of inequalities, solving inequalities,solving compound inequalities, solving open sentencesinvolving absolute value, and graphing inequalities in twovariables.
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer may be given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
An
swer
s
© Glencoe/McGraw-Hill A26 Glencoe Algebra 1
Chapter 6 Assessment Answer KeyPage 391, Open-Ended Assessment
Sample Answers
2a. After drawing a graph, studentsshould write an inequality thatcorresponds with the line they havedrawn. The inequality may or may notinclude equality.
2b. The solution set includes the boundary(line) if the inequality written for parta includes equality. If the inequalitywritten for part a does not includeequality, then the student should statethat the solution set of the inequalitydoes not include the line.
3. The inequality ab � 2a can bedetermined to be true or false byconsidering the value of a. Since b � 2,by the Multiplication Property ofInequality ab � 2a is true if a is apositive number.
4a. � x � � 3 means the distance from 0 to xis 3 units. The only values for x thatsatisfy this statement are x � �3 andx � 3. Thus, the solution set is {�3, 3}.
4b. The solution set for � x � 2 � � 4 is {x � x � �2 or x � 6}. The solution setfor �2x � 4 or x � 6 is {x � x � �2}.One includes numbers greater than�2, and the other includes numbersless than �2 or greater than 6. Thesesolution sets are not the same.
5a. w � 90 � 2(20); {w � w � 50}5b. The formula for the area of a rectangle
with 50 substituted for the width can be used to write the compound inequality 2800 � 50� � 3200. The possiblelengths are found by solving thiscompound inequality for �. Thesolution set is {� � 56 � � � 64}.
5c. � 175,000 � x � � 20,000;155,000 � x � 195,000;The Fraziers are willing to pay from$155,000 to $195,000 for the house.
In addition to the scoring rubric found on page A25, the following sample answers may be used as guidance in evaluating open-ended assessment items.
1. 10n � 7(n � 2) � 5n � 12 Original inequality10n � 7n � 14 � 5n � 12 Distributive Property
3n � 14 � 5n � 12 Combine like terms.3n � 14 � 5n � 5n � 12 � 5n Subtract 5n from each side.
�2n � 14 � �12 Simplify.�2n � 14 � 14 � �12 � 14 Add 14 to each side.
�2n � 2 Simplify.
���22n
� � 2 (�2) Divide each side by �2.
n � �1 Simplify.
The solution set is {n�n � �1}.
© Glencoe/McGraw-Hill A27 Glencoe Algebra 1
1. true
2. false; equation
3. false; or
4. false; negative
5. true
6. true
7. false; positive
8. true
9. true
10. false; intersection
11. Multiply both sidesof the inequality by
��32
� and change �
to �.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Quiz (Lesson 6–3)
Page 393
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
Quiz (Lesson 6–6)
Page 394
1.
2.
3.
4. 35x 25y � 230;No, the cost isgreater than $230.
y
xO
{(0, 1), (�1, 2)}
�x � � 1
{�4, �1}
0 1 2 4 5 6 7 83
{y �y � 5 or y � 6}
�1�2�3�4�5�6 0 1 2
{x ��5 � x � 0}
{y � y � 1}
{y � y � 3}
{d � d � �100}
B
{w �w � �2.3}
{n � n � �28}
�r � r � 1�115��
{m � m � �78}
�m�m � �12
��{r � r � 0}
13121110 14 15 17 1816
{w � w � �14}13121110 14 15 17 1816
{n � n � 14}
Chapter 6 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 6–1 and 6–2) Quiz (Lessons 6–4 and 6–5)
Page 392 Page 393 Page 394
An
swer
s
Sample answer:n � the number;n 3 � 19 � n; {n � n � 8}
Sample answer:n � the number;n � 7 � 15; {n � n � 22}
Sample answer:x � the number;16 � 8x � 40; {x � 2 � x � 5}
y
xO
© Glencoe/McGraw-Hill A28 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
�1�2�3�4 0 1 2 43
�x � �3 � x � �13
��;
let n � the number;2n � 7 � �5 or 2n � 7 � 13;{n � n � 1 or n � 10}
{u � u � 18}
�1�2�3�4 0 1 2 43
{r � r � 3};
y
xO 1
123456789
2 3 4 5 6 7 8 9
y � 3x 5
d � 55t; 275 miles
��87
�
yes; common difference is 3
{(1, �2), (�1, 3), (�2, 2), (0, �2)}
X
�2
3
�10
�1�22
Y
decrease; 25%
�29
�
whole number, integer,rational number
32y 38
Sample answer:a � no. of apples;6a � 50;
at least 8�13
� apples
Sample answer:� � length; � 63 � 85;22 in. or less
�v � v � �49
��{t � t � 15.2}
C
B
D
C
Chapter 6 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 395 Page 396
negative correlation
© Glencoe/McGraw-Hill A29 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. 11.
12. 13.
14.
15.
16. DCBA
DCBA
DCBA
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
2 5
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
8
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
. 7 56
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
7 / 2
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
Chapter 6 Assessment Answer KeyStandardized Test Practice
Page 397 Page 398
An
swer
s
© Glencoe/McGraw-Hill A30 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20. B
B
C
D
A
B
C
C
D
B
A
B
D
A
C
B
C
D
A
D
Chapter 6 Assessment Answer KeyFirst Semester Test
Page 399 Page 400
(continued on the next page)
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47. {�10, 3}�4�3�2�1 0 2 3 4 5 6 71
{x � x � �2 or x � 5};
{x � x � �2}
{t � t � 3}
Sample answer using(4, 80) and (10, 29):
y � ��127�x � 114
negative correlation
1
�34
�; �2; �83
�
C � 1.9n
an � 4n � 3
y
xO
y � 2x – 3
{(�4, 2), (�4, �3),(0, �3), (2, 0), (3, 1)};
{(2, �4), (�3, �4),(�3, 0), (0, 2), (1, 3)}
dilation
310 mph
increase; 15%
�45
�
2
36
3:1
4.4
�28xy � 4uv
{�1, 0, 1, 2, 3, 4, 5, 6, …}
You could visit an artgallery that has no paintings by Monet.
1.8x � 10.9y
Additive InverseProperty; �5
{1, 2, 3}
11
An
swer
s
© Glencoe/McGraw-Hill A31 Glencoe Algebra 1
Chapter 6 Assessment Answer KeyFirst Semester Test (continued)
Page 401 Page 402