chapter 7 resource masters -...

Chapter 7Resource Masters

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce thematerial contained herein on the condition that such material be reproduced onlyfor classroom use; be provided to students, teacher, and families without charge;and be used solely in conjunction with Glencoe Pre-Algebra. Any other reproduc-tion, for use or sale, is prohibited without prior written permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240

ISBN: 0-07-827773-6

1 2 3 4 5 6 7 8 9 10 047 11 10 09 08 07 06 05 04 03 02 Pre-Algebra Chapter 7 Resource Masters

Consumable Workbooks

Many of the worksheets contained in the Chapter Resource Masters booklets are

available as consumable workbooks in both English and Spanish.

Study Guide and Intervention Workbook 0-07-827794-9

Study Guide and Intervention Workbook (Spanish) 0-07-827795-7

Skills Practice Workbook 0-07-827788-4

Skills Practice Workbook (Spanish) 0-07-827790-6

Practice Workbook 0-07-827789-2

Practice Workbook (Spanish) 0-07-827791-4

Answers for Workbooks The answers for Chapter 7 of these workbooks

can be found in the back of this Chapter Resource Masters booklet.

Spanish Assessment Masters Spanish versions of forms 2A and 2C

of the Chapter 7 Test are available in the Pre-Algebra Spanish Assessment

Masters (0-07-830412-1).

iii

Vocabulary Builder............................vii

Lesson 7-1Study Guide and Intervention ........................367Skills Practice.................................................368Practice ..........................................................369Reading to Learn Mathematics ......................370Enrichment .....................................................371






Chapter 7 AssessmentChapter 7 Test, Form 1 ..........................397–398Chapter 7 Test, Form 2A........................399–400Chapter 7 Test, Form 2B........................401–402Chapter 7 Test, Form 2C........................403–404Chapter 7 Test, Form 2D........................405–406Chapter 7 Test, Form 3 ..........................407–408Chapter 7 Open-Ended Assessment .............409Chapter 7 Vocabulary Test/Review ................410Chapter 7 Quizzes 1 & 2................................411Chapter 7 Quizzes 3 & 4................................412Chapter 7 Mid-Chapter Test...........................413Chapter 7 Cumulative Review .......................414Chapter 7 Standardized Test Practice....415–416

Standardized Test Practice Student Recording Sheet ..............................................A1ANSWERS ................................................A2–A26

CONTENTS

iv

Teacher’s Guide to Using theChapter 7 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resources youuse most often. The Chapter 7 Resource Masters includes the core materials needed forChapter 7. These materials include worksheets, extensions, and assessment options. Theanswers 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 the Pre-Algebra TeacherWorks CD-ROM.

Vocabulary Builder Pages vii-viiiinclude a student study tool that presents up to twenty of the key vocabulary termsfrom the chapter. Students are to record definitions and/or examples for each term.You may suggest that students highlight or star the terms with which they are not familiar.

When to Use Give these pages to studentsbefore beginning Lesson 7-1. Encourage themto add these pages to their Pre-Algebra StudyNotebook. Remind them to add definitionsand examples as they complete each lesson.

Study Guide and InterventionEach lesson in Pre-Algebra addresses one ortwo objectives. There is one Study Guide andIntervention master for each lesson.

When to Use Use these masters as reteach-ing activities for students who need addi-tional reinforcement. These pages can alsobe 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 usedwith students who have weaker mathematicsbackgrounds or need additional reinforcement.

Practice There is one master for each lesson. These problems more closely followthe structure of the Practice and Apply section of the Student Edition exercises.These exercises are of average difficulty.

When to Use These provide additionalpractice options or may be used as home-work for second day teaching of the lesson.

Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lesson inthe Student Edition. Additional questionsask students to interpret the context of andrelationships among terms in the lesson.Finally, students are asked to summarizewhat they have learned using various repre-sentation techniques.

When to Use This master can be used as a study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner)students.

Enrichment There is one extension master for each lesson. These activities may extend the concepts in the lesson, offeran historical or multicultural look at theconcepts, or widen students’ perspectives on the mathematics they are learning.These are not written exclusively for honorsstudents, but are accessible for use with alllevels of students.

When to Use These may be used as extracredit, short-term projects, or as activitiesfor days when class periods are shortened.

v

Assessment OptionsThe assessment masters in the Chapter 7Resource 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 level student. 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 testing situa-tions. Grids with axes are provided forquestions 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 rubric isincluded for evaluation guidelines. Sampleanswers are provided for assessment.

• A Vocabulary Test, suitable for all stu-dents, 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 appropriate inter-vals 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 Pre-Algebra. It can also be used as a test. This master includesfree-response questions.

• The Standardized Test Practice offerscontinuing review of pre-algebra conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and open-ended questions.Bubble-in and grid-in answer sections areprovided on the master.

Answers• Page A1 is an answer sheet for the

Standardized Test Practice questions that 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-lesson masters are provided as reduced pageswith answers appearing in red.

• Full-size answer keys are provided for theassessment masters in this booklet.

vii

This is an alphabetical list of key vocabulary terms you will learn in Chapter 7.As you study this chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Pre-Algebra Study Notebook to review vocabulary at the end of the chapter.

Reading to Learn MathematicsVocabulary Builder

NAME ______________________________________________ DATE ____________ PERIOD _____

77

Vocabulary FoundDefinition/Description/ExampleTerm on Page

identity

inequalityIHN-ih-KWAHL-uht-ee

null or empty setNUHL

Vo

cab

ula

ry B

uild

er

Solve each equation. Check your solution.

1. 2x � 1 � x � 11 2. a � 2 � 5 � 4a 3. 7y � 25 � 2y

4. n � 11 � 2n 5. 7 � 4c � 3c � 7 6. 4 � 3b � 6b � 5

7. 9d � 9 � 3d � 3 8. f � 4 � 6f � 26 9. �2s � 3 � 5s � 24

10. 5a � 3 � 8a � 6 11. 8n � 12 � �12n � 8 12. 7y � 8 � �2y � 64

13. 1 � 3x � 7x � 7 14. 6a � 3 � 4 � 7a 15. 3b � 1 � 14 � 2b

16. 12c � 18 � 4 � 5c 17. 9y � 3 � 5y � 13 18. 3n � 2 � 5n � 12

ExercisesExercises

To solve equations with variables on each side, use the Addition or Subtraction Property of Equality towrite an equivalent equation with the variable on one side. Then solve the equation.

12x � 3 � 4x � 13 Write the equation.

12x � 4x � 3 � 4x � 4x � 13 Subtract 4x from each side.

8x � 3 � 13 Simplify.

8x � 3 � 3 � 13 �3 Add 3 to each side.

8x � 16 Simplify.

x � 2 Mentally divide each side by 8.

To check your solution, replace x with 2 in the original equation.

CHECK

12x � 3 � 4x � 13 Write the equation.

12(2) � 3 � 4(2) � 13 Replace x with 2.

24 � 3 � 8 � 13 Check to see whether the statement is true.

21 � 21 The statement is true.

ExampleExample

Study Guide and InterventionSolving Equations with Variables on Each Side

NAME ______________________________________________ DATE ____________ PERIOD _____

7-17-1

© Glencoe/McGraw-Hill 367 Glencoe Pre-Algebra

Less

on

7-1

Solve the equation 12x � 3 � 4x � 13. Then check your solution.


Skills PracticeSolving Equations with Variables on Each Side

NAME ______________________________________________ DATE ____________ PERIOD _____

7-17-1


1. 3x � 2 � 5x 2. n � 12 � 3n

3. 2 � 3b � 7b � 12 4. 4d � 11 � 2d � 7

5. 2f � 3 � 11f � 24 6. 8y � 11 � 2y � 29

7. 5a � 45 � 2a 8. 17 � 3c � 4c � 3

9. 2a �3 � 9a � 10 10. 5b � 21 � 4b

11. 9y � 27 � �2y � 6 12. 2n � 5 � 7n

13. �s � 3 � 5s � 21 14. 7 � 4c � 3c � 35

15. 30 � 2n � 4n 16. 29 � 7d � 5d � 15

17. 16k � 23 � 6k � 13 18. w � 20 � 6w

19. 33g � 28 � 25g �12 20. 6h �34 � �6h � 14

21. 3t � 17 � t � 3 22. 11 j � 6 j �15

23. c � 2 � 3c � 14 24. 28x � 7 � 26x � 5

25. 5m � 6 � 8m � 9 26. �4p � 7 � 5p � 11

27. �10 � 3 f � 5 f � 6 28. 4 f � 6 � 8 f � 14

29. �7n � 16 � 4n � 17 30. 5d � 9d � 18

Define a variable and write an equation to find each number. Then solve.

31. Three times a number equals 40 more than five times the number. What is the number?

32. A number equals four less than three times the number. What is the number?

33. Eight times a number equals 24 more than two times the number. What is the number?

PracticeSolving Equations with Variables on Each Side

NAME ______________________________________________ DATE ____________ PERIOD _____

7-17-1



1. 3g � 12 � 9g 2. 14m � 18 � 12m

3. 7c � 7 � 4c � 17 4. �11t � 15 � 6t

5. 20s � 4 � 13s � 10 6. �2h � 16 � 3h � 6

7. 27j � 6 � 14j � 7 8. �1 � 19w � 11w � 23

9. 8 � p � �12 � 3p 10. 9k � 26 � 6k � 8

11. 28 � 4d � 5d � 17 12. 2y � 7 � y

13. 11.7 � 2x � x 14. 3b � 4.4 � 2.6 � 6b

15. �34

� y � 6 � �14

� y � 10 16. 2c � 7.5 � 6.2 � 3c

17. 5d � 11 � 2d � 2 18. 6a � 10 � 2a � 7

19. 8n � 6 � �9n � 11 20. 2f � 9 � 14f � 1

Define a variable and write an equation to find each number. Then solve.

21. Twice a number is 60 more than five times the number. What is the number?

22. Four times a number is 21 more than the number. What is the number?

23. Eight less than three times a number equals the number. What is the number?

24. A number equals six less than four times a number. What is the number?

25. TENNIS The area of a tennis court is 2808 ft2, or 8 square feet more than 3.5 times thesize of the area of a racquetball court. What is the area of a raquetball court?

26. CELLULAR PHONES One cellular phone carrier charges $26.50 a month plus $0.15 aminute for local calls. Another carrier charges $14.50 a month and $0.25 a minute forlocal calls. For how many minutes is the cost of the plans the same?

Less

on

7-1


Reading to Learn MathematicsSolving Equations with Variables on Each Side

NAME ______________________________________________ DATE ____________ PERIOD _____

7-17-1

How is solving equations with variables on each side likesolving equations with variables on one side?

Do the activity at the top of page 330 in your textbook. Write youranswers below.

a. The two sides balance. Without looking in a bag, how can you determine the number of blocks in each bag?

b. Explain why your method works.

c. Suppose x represents the number of blocks in the bag. Write an equation that is modeled by the balance.

d. Explain how you could solve the equation.

Pre-Activity

Reading the Lesson

Describe in words each step shown for solving the following equation.

1. 2x � 4 � 4x � 8

2. 2x � 2x � 4 � 4x � 2x � 8

3. 4 � 2x � 8

4. 4 � 8 � 2x � 8 � 8

5. 12 � 2x

6. �122� � �

22x�

7. 6 � x

Helping You Remember

8. Write out an equation like that shown above (2x � 4 � 4x � 8), along with all the steps needed to solve the equation. Exchange equations with a partner. Then each of you should explain verbally why each step in solving the equation was carried out, forexample, “2x was subtracted from each side to eliminate the variable on the left side.”

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

7-17-1


Fractional EquationsTo solve equations containing fractions, multiply both sides by the least common denominator. Then solve as usual.

Solve �25x� � �

1x0� � 6.

�25x� � �

1x0� � 6 The least common denominator is 10.

10 ��25x� � �

1x0�� 10(6)

10��25x�� 10��

1x0�� 10(6)

4x � x � 10(6)

3x � 60

�33x� � �

630�

x � 20

Solve each equation.

1. �32x� � x � 1 2. �

38x� � �

3x

� � �43

�

3. �6y

� � �4y

� � 5 4. 2a � �a3

� � �a4

� � 5

5. �x �

32

� � �x �

41

� 6. �x �

21

� � �x �

32

� � 1

7. �x �

53

� � �x

1�

52

� � �23

� � 0 8. �x �

34

� � 4 � �x �

411�

9. ��d4

� � d � �18

� 10. �x �

57

� � 2 � �x

1�

08

�

11. z � �4z

� � 14 � �2z

� 12. �y

1�

63

� � �y �

64

� � �13

�

ExampleExample

Less

on

7-1


Equations with grouping symbols can be solved by first using the Distributive Property to remove thegrouping symbols.

2(6m � 1) � 8m Write the equation.

12m � 2 � 8m Apply the Distributive Property.

12m � 12m � 2 � 8m � 12m Subtract 12m from each side.

�2 � �4m Simplify.

��

�

24� � �

�

�

44m� Divide each side by –4.

�12

� � m Simplify.

CHECK

2(6m � 1) � 8m

2�6��12

�� 1� � 8(�12

�) Replace m with �12

�.

2(3 � 1) � 4 Simplify.

4 � 4� The solution checks.

Some equations have no solution. The solution set is the null or empty set. Other equations have every number as a solution. Such an equation is called an identity.


1. 8( g � 3) � 24 2. 5(x � 3) � 25 3. 7(2c � 5) � 7 4. 2(3d � 7) � 5 � 6d

5. 2(s � 11) � 5(s � 2) 6. 7y � 1 � 2(y � 3) � 2 7. 2( f � 3) � 2 � 8 � 2f

8. 2(x � 2) � 3 � 2x � 1 9. 1 � 2(b � 6) � 5(b � 1) 10. 2x � 5 � 3(x � 3)

Study Guide and InterventionSolving Equations with Grouping Symbols

NAME ______________________________________________ DATE ____________ PERIOD _____

Example 1Example 1

ExercisesExercises

7-27-2

Example 2Example 2

a. 2(x � 1) � 4 � 2x b. �2(x � 1) � 2 � 2x

�2x � 2 � 4 � 2x �2x � 2 � 2 � 2x

2x � 2x � 2 � 4 � 2x � 2x �2x � 2 � 2 � 2 � 2 � 2x

�2 � 4 �2x � �2xThe solution set is Ø. x � x

The solution set is all real numbers.

Solve the equation 2(6m � 1) � 8m. Check your solution.

Solve each equation.

Skills PracticeSolving Equations with Grouping Symbols

NAME ______________________________________________ DATE ____________ PERIOD _____

7-27-2



1. 2( g � 7) � 16 2. 5(x � 2) � 30

3. 3(2d � 7) � 39 4. 4(a � 2) � 3(a � 4)

5. 3( f � 2) � 9 � 13 � 5f 6. 2(x �4) � 3(1 � x)

7. 2n � 5 � 4(n � 2) � n 8. 4(x � 3) � x

9. 2(c � 3) � 76 10. 7(x � 2) � 5(x � 2)

11. 2(6x � 1) � 4(x � 5) � 2 12. 4(2b � 6) � 11 � 8b � 13

13. 6 � 6(2t � 1) � 3 � 12t 14. 9t � 21 � 3(t � 7) � 6t

15. 3(4k � 14) � 10k � 2(k � 7)

Find the dimensions of each rectangle. The perimeter is given.

16. P � 380 m

17. P � 640 yd

18. P � 220 ft

19. P � 380 yd

20. P � 300 m

w

w � 20

w

3w � 12

w

2w � 40

w

5w � 10

�1�2 0 1 2 4 5 63

Less

on

7-2


PracticeSolving Equations with Grouping Symbols

NAME ______________________________________________ DATE ____________ PERIOD _____

7-27-2


1. 4( j � 7) � 12 2. 5(2k � 10) � 40

3. 7(2p � 3) � 8� 6p � 29 4. 7( g � 4) � 3

5. 3(4c � 5) � 24 6. 2(a �1) � 3(a � 1)

7. 3(x � 3) � 5(1.5 � x) 8. 2(1.5m � 3) � 3.5m � 1

9. a � �150� � 2a � �

35

� 10. 2.2x � 5 � 2(1.4x � 3)

11. �0d.2� � 3d � 2.1 12. 5n � 3 � 2(n � 2) � 3n

13. �23

�a � 2 � �13

�(4 a � 1) 14. y � 7 � �14

�(y � 2)

15. 5( f � 2) � 9 � 5f

Find the dimensions of each rectangle. The perimeter is given.

16. P � 122 m

17. P � 244 yd

18. P � 698 cm

19. P � 86 in

20. GEOMETRY The perimeter of a rectangle is 80 feet. Find the dimensions if the length is5 feet longer than four times the width. Then find the area of the rectangle.

21. NUMBER THEORY Five times the sum of three consecutive integers is 150. What are theintegers?

w

w � 35

w

3w � 18

w

w � 23

w

w � 3

Reading to Learn MathematicsSolving Equations with Grouping Symbols

NAME ______________________________________________ DATE ____________ PERIOD _____

7-27-2


Why is the Distributive Property important in solving equations?


a. What does t represent?

b. Why is Maria’s time shown as t � 1?

c. Write an equation that represents the time when Maria catches up to Josh. (Hint: They will have traveled the same distance.)

Pre-Activity

Reading the LessonWrite a definition and give an example of each new vocabulary word or phrase.

3. If an equation results in a sentence that is never true, the solution set

is .

4. When an equation results in an identity, the solution set

is .

5. To solve an equation containing grouping symbols, you must first use

the .

6. For a rectangle, two times the length plus two times the width equals

the .


7. Explain in a paragraph why solving a geometry problem, like that in Example 2 in yourtext, requires the use of the Distributive Property. You may wish to sketch a figure andassign values to the sides to aid your explanation.

Vocabulary Definition Example

1. null or empty set

2. identity Less

on

7-2


Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

7-27-2

Sonya Vasilievna KovaleskySonya Vasilievna Kovalevsky (1850�1891), a Russian mathematician, achieved a good education and a successful career despite the disadvantage at that time of being female.Discover her accomplishments by working the problems at the bottom of the page. Then ifyou find your answer in the chart, circle the fact in that square. Each circled fact is a truestatement about Kovalevsky’s life.

1. 2z � 8 � 12 2. 28 � 11x � 5 3. n � 12 � 54 � n

4. 3x � 8 � 5x � 6 5. 6 � 2s � 7 6. �9x

� � 3 � 17

7. 9 � (2a � 6) � �9 8. x � 6 � 5 � x 9. x � 3(2x � 1) � 4(2x � 1)

SONYA VASILIEVNA KOVALEVSKY (1850–1891)

She was denied aneducation in Russia.

Sonya was a Russianmathematician andphysicist.

She became a Lecturer andlater Professor of HigherMathematics in Stockholm.

She began her formal studyat the Naval Academy in St.Petersburg.

She was taught privatelyby renownedmathematician KarlWeierstrass in Berlin.

She wrote a play that wasproduced in Moscow.

Sonya was born in Polandand became a well-knownmathematician andnovelist.

She was married just sothe European universitieswould allow her to attendhigher education classes.

Upon receiving herdoctorate, she was offeredseveral professionalappointments all overEurope.

3

10

612

156

�5

14

33

12

�

Write an inequality for each sentence.

1. Your age is greater than 12 years.

2. A number decreased by 25 is no more than 65.

3. More than $1000 was collected for the charity.

4. At least 80 runners showed up for the charity race.

Graph each inequality on a number line.

5. x � 7 6. a � �2 7. d � �4

8. w � �9 9. t � �5 10. n � �11

ExercisesExercises

Example 2Example 2

a. x � 8 b. x � 8

The open circle means The closed circle meansthe number 8 is not the number 8 isincluded in the graph. included in the graph.

A mathematical sentence that contains any of the symbols listed below is called an inequality.

a. Less than 70 students attended the last dance.

b. At the store, the camera cost at least as much as the mail-order price of $229.

Graph an inequality on a number line to help visualize the values that make the inequality true.

Example 1Example 1

Study Guide and InterventionInequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

7-37-3


� � � �

• is less than • is greater than • is less than or • is greater thanequal to or equal to• is fewer than • is more than

• is no more than • is no less than• exceeds• is at most • is at least

6 7 8 9 10 109876

5 6 7 8 9 �4 �3 �2 �1 0 �6 �5 �4 �3 �2

�9 �8 �7�11 �10 �5�6�7 �4 �3 �9�13 �12 �11 �10

Less

on

7-3




Skills PracticeInequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

7-37-3


1. More than 100,000 fans attended the opening football game at The Ohio StateUniversity.

2. Her earnings at $16 per hour were no more than $96.

3. A savings account decreased by $50 is now less than $740.

4. A number increased by 7 is at least 45.

For the given value, state whether each inequality is true or false.

5. �1c8� � 9, c � 2 6. �

5x

� � 3, x � 5

7. 6k � 42, k � 7 8. 10 � x � 3, x � 7

9. 11 � n � 32, n � 4 10. 9 � c � 19, c � 10


11. a � 6 12. t � �2 13. d � 3

14. b � 10 15. x � �7 16. x � 2

Write the inequality for each graph.

17. 18.

19. 20.

21. 22.

7 8654 �2�3�4 �1 0 4 5321

12111098 �7�8�9 �6 �5 43210

12111098 �4 �3 �2 �1 0

�9 �8 �7 �6 �5 87654

3 4210 �38 �37 �36�40 �39

PracticeInequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

7-37-3



1. More than 3400 people attended the flea market.

2. Her earnings at $11 per hour were no more than $121.

3. The 10-km race time of 84 minutes was at least twice as long as the winner’s time.

4. A savings account increased by $70 is now more than $400.

For the given value, state whether each inequality is true or false.

5. 9 � x � 3, x � 6.5 6. 9.5 � n � 19, n � 10

7. 3k � 27 �12

�, k � 8 8. 21 � 4c, c � 5.2

9. �4x

� � 8, x � 32 10. �9c

� � 2, c � 3 �12

�


11. a � �2 12. t � �6 13. d � 7

14. b � 11 15. x � �8 16. w � 5

17. n � 20 18. b � �4 19. a � �6

Write the inequality for each graph.

20. 21.

22. 23.

�4 �3 �2 �1 0

�3�4�5 �2 �114 15131211

76543

�6�7�8 �5 �4

2221201918 �6 �5 �4 �3 �2 �8 �7 �6 �5 �4

98765

�9 �8 �7 �6�10131211109

96 7 85�20 �19 �18 �17 �16Le

sso

n 7

-3


Reading to Learn MathematicsInequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

7-37-3

How can inequalities help you describe relationships?

Do the activity at the top of page 340 in your textbook. Writeyour answers below.

a. Name three ages of children who can eat free at the restaurant. Doesa child who is 6 years old eat free?

b. Name three heights of children who can ride the ride at the amusement park. Can a child who is 40 inches tall ride?

c. Name three speeds that are legal. Is a driver who is traveling at 35 mph driving at a legal speed?

Pre-Activity

Reading the LessonWrite a definition and give an example of the new vocabulary word.

For each of the following phrases, write in the blank the corresponding inequality symbol. Use �, �, � , or � .

2. is greater than 3. is less than or equal to

4. is at least 5. is no less than

6. exceeds 7. is less than

8. is more than 9. is at most


10. The word inequality is composed of the prefix in- and the base word equality.

a. Find the definitions of in- and equality in a dictionary. Write their definitions.

b. Explain how the definitions can help you remember how inequality is usedin mathematics.

Vocabulary Definition Example

inequality1.

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

7-37-3


Make Up a ProblemYou have seen that some problem situations can be solved using variables and open sentences. Usually in math, you are asked to solve problems. In this activity, you will bewriting the problems.

Use the open sentence, story idea, and your imagination to write an interestingword problem.

1. x � 4 � 83

scores on a chapter test

2. 15 � x � 10

money spent on clothes

3. 12 � v � 20

a team’s win/loss record

4. 9 � p � 10

people at a party

5. 13 � y � 21

ages

6. 36 � h � 47

temperaturesLe

sso

n 7

-3


Use the Addition and Subtraction Properties of Inequalities to solve inequalities. When you add or subtract a number from each side of an inequality, the inequality remains true.

Solve 12 � y � 20. Check your solution.

12 � y � 20 Write the inequality.

12 � 12 � y � 20 � 12 Subtract 12 from each side.

y � 8 Simplify.

To check your solution, try any number greater than 8.

CHECK

12 � y � 20 Write the inequality.

12 � 9 � 20 Replace y with 9.

21 � 20 This statement is true.

Any number greater than 8 will make the statement true. Therefore, the solution is y � 8.

Solve each inequality. Check your solution.

1. �12 � 8 � b 2. t � 5 � �4 3. p � 5 � �13

4. 5 � �6 � y 5. 21 � n � (�18) 6. s � 4 � 3

7. 14 � w � (�2) 8. j � 6 � �4 9. z � (�4) � �2.5

10. b � �14

� � 2 �14

� 11. g � 2 �13

� � 3 �16

� 12. �2 � z � 5

13. �10 � x � 5 14. �23 � a � (�6) 15. 20 � m � 6

16. 1 �12

� � b � 7 17. k � 5 � �7 18. � �23

� � w � 2

Study Guide and InterventionSolving Inequalities by Adding or Subtracting

NAME ______________________________________________ DATE ____________ PERIOD _____

ExampleExample

ExercisesExercises

7-47-4

?

?

Skills PracticeSolving Inequalities by Adding or Subtracting

NAME ______________________________________________ DATE ____________ PERIOD _____

7-47-4



1. p � 9 � 13 2. t � 7 � �4 3. �12 � 7 � x 4. f � (�7) � 9

5. 5 � �3 � y 6. r � 7 � �3 7. b � 15 � 11 8. z � (�4) � �8

9. j � 4 � �10 10. �5 � h �3 11. 13 � w � (�14) 12. g �7 � �4

13. �15 � d � (�2) 14. 2 � c � �8 15. 15 � c � 3 16. j � 9 � �10

Solve each inequality. Then graph the solution on a number line.

17. n � 6 � 7 18. �4 � z � 3 19. p � (�3) � �6

20. �11 � x � 8 21. 15 � m � (�2) 22. k � 7 � �9

23. �5 � 2 � a 24. t �7 � 5 25. �2 � z � 7

26. p � (�7) � �8 27. �6 � m � 2 28. �2 � w � 5

29. SHOPPING Chantal would like to buy a new pair of running shoes. Shoes that she likesstart at $85. If she has already saved $62, what is the least amount she must still save?

11109871413121110�7�8�9 �6 �5

1 2 3 4 5�10 �9 �8 �7 �6�17 �16 �15 �14 �13

�18 �17 �16 �15 �141514131211�21 �20 �19 �18 �17

�3�4�5 �2 �198765�1 2 310

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PracticeSolving Inequalities by Adding or Subtracting

NAME ______________________________________________ DATE ____________ PERIOD _____

7-47-4


1. h � 1 � 7 2. c � 3 � �4 3. 22 � m � 9

4. �6 � g � 4 5. 15 � d � 10 6. p � (�8) � �12

7. �13 � k � (�16) 8. �1 � s � 5 9. 12 � w � (�0.3)

10. �1 �78

� � d � (�2) 11. z � 0.9 � �4.8 12. b � �15

� � 3 �110�

Solve each inequality. Then graph the solution on a number line.

13. 5 � a � 16 14. c � 12 � 14

15. �20 � h � 3 16. 16 � k � (�17)

17. p � (�2) � �4 �12

� 18. �2 � z � 3 �34

�

19. TRANSPORTATION A certain minivan has a maximum carrying capacity of 1200 pounds. If the luggage weighs 150 pounds, what is the maximum weight allowable for passengers?

20. DRINKS A large punch bowl holds 12 gallons of liquids. If five gallons of ginger ale havealready been poured into the bowl, what is the most fruit juice that can be added?

21. FUND-RAISING A neighborhood association wants to replace the playground equipmentat a park. The playground equipment they would like to buy starts at $4500. If theyhave already raised $2700, what is the least they must still collect?

131211109 3 4210

�19 �18 �17 �16 �15 34 35333231

�6�7�8 �5 �4 6 7543

Reading to Learn MathematicsSolving Inequalities by Adding or Subtracting

NAME ______________________________________________ DATE ____________ PERIOD _____

7-47-4


How is solving an inequality similar to solving an equation?


a. How many blocks would be in the bag if the left side balanced the rightside? (Assume that the paper bag weighs nothing.)

b. Explain how you determined your answer to part a.

c. What numbers of blocks can be in the bag to make the left side weighless than the right side?

d. Write an inequality to represent your answer to part c.

Pre-Activity

Reading the Lesson

1. Describe the Addition Property of Inequality and give an example of a problem thatrequires its use.

2. Describe the Subtraction Property of Inequality and give an example of a problem thatrequires its use.

3. Is 6 a solution for the inequality 17 � x > 23? Explain.


4. In each box below, write three inequalities that can be solved by using the given property.Include at least one negative integer in each box.

Addition Propertyof Inequality

Subtraction Propertyof Inequality

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ExampleExample


Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

7-47-4

Solving Inequalities Using Addition and SubtractionInequalities can be written many different ways in English.

English Phrase Mathematical Phrase

at most x � x

at least x � x

5 less than x x � 5

5 more than x x � 5

5 is less than x 5 � x

x is between 4 and 6 4 � x � 6 or x � 4 and x � 6

1. Write a mathematical phrase for each of the following English phrases.

a. 8 more than x.

b. x is at least 3.

c. x is between 6 and 12.

d. x cannot exceed �5.

2. For what values of x, if any, is the mathematical phrase 5 � x � 7 true?

To solve compound inequalities, you must perform the same operation on each of the threeparts of the inequality.

Solve the compound inequality 3 � x � 2 � 5.

3 � x � 2 � 5

3 � 2 � x � 2 � 2 � 5 � 2 To get x by itself, add 2 to each part.

5 � x � 7

Thus, x is all numbers between 5 and 7.

Solve each compound inequality.

3. �2 � x � 1 � 4 4. �4 � x � 1 � 0

5. 3 � 15 � x � 10 6. �12 � x � 3 � 1

Solve each inequality and check your solution. Then graph the solution on a number line.1. 81 � 9d 2. �

p3

� � �12 3. ��

h4� � 3

4. �20t � 100 5. ��

3x2� � 12 6. �16 � � �

14

�b

7. �8 � ��2

c.5� 8. �

n3

� � 0.5

ExercisesExercises

Example 2Example 2 Solve ��

y

12� � 4 and check your solution. Then graph the solution on

a number line.

��

y12� � 4 Write the inequality.

�12��

y12�� 12(4) Multiply each side by –12 and reverse the symbol.

y � �48 Check the result.

Graph the solution, y � �48.

Use the Multiplication and Division Properties of Inequalities to solve inequalities. When you multiply ordivide each side of an inequality by a positive number, the inequality remains true. The direction of theinequality sign does not change.

Solve 8x � 72. Check your solution.

8x � 72 Write the inequality.

�88x� � �

782� Divide each side by 8.

x � 9 Simplify.

The solution is x � 9. You can check this solution by substituting 9 or a number greater than9 into the inequality.

For an inequality to remain true when multiplying or dividing each side of the inequality by a negativenumber, however, you must reverse the direction of the inequality symbol.

Example 1Example 1

Study Guide and InterventionSolving Inequalities by Multiplying or Dividing

NAME ______________________________________________ DATE ____________ PERIOD _____

7-57-5


�48 �47 �46�50 �49

1110987 �38 �37 �36 �35 �34 �14 �13 �12 �11 �10

�5�7 �6 �4 �3 �20 �19 �18 �17 �16 65 66646362

21 22201918 43210

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Skills PracticeSolving Inequalities by Multiplying or Dividing

NAME ______________________________________________ DATE ____________ PERIOD _____

7-57-5

Solve each inequality and check your solution. Then graph the solution on a number line.

1. �8x � 16 2. 7y � �35

3. 12a � �24 4. �12 � 4a

5. �6z � �18 6. 14 � �2k

7. 5 � ��

x2� 8. �

�

r3� � �4

9. �10 t � 200 10. �7y

� � 2

11. ��

21� x � �6 12. �

�

b3� � 6

13. TRAVEL To get to the beach for vacation, Cheng’s family must drive at least 660 mileson the first day. They are traveling at a constant speed of 60 miles per hour.

a. Write an inequality to represent how long the family should drive on the first day.

b. How many hours should the family drive?

14. EARNINGS Jess receives $180 for every garage he paints over the summer. He wants tosave at least $1620 for college.

a. Write an inequality to represent how many garages Jess should paint over the summer.

b. How many garages should Jess paint?

�4 �3 �2 �1 0 �7 �6 �5 �4 �3

�2�4 �3 �1 0 �3�5 �4 �2 �1

54321 �7�8�9 �6 �5

�9 �8�12 �11 �10 1413121110

�22 �21 �20 �19 �18 15 16141312

1413121110 �20 �16�17�18�19

PracticeSolving Inequalities by Multiplying or Dividing

NAME ______________________________________________ DATE ____________ PERIOD _____

7-57-5


Solve each inequality and check your solution. Then graph the solution on a number line.

1. 9x � 18 2. 10 d � 80

3. 25 � 5c 4. �1t3� � 3

5. 24 � ��

g4� 6. �78 � 6h

7. ��

f5� � �12 8. 100 � �4s

9. ��

p36� � 6 10. �4 � �

�3c.5�

11. �24 � �21b� 12. �3 � �

�1c.5�

13. DISCOUNTS To qualify for a store discount, Jorge’s soccer team must spend at least$560 for new jerseys. The team needs 20 jerseys.

a. Write an inequality to represent how much the team should spend on each jersey toqualify for the discount.

b. How much should the team spend for each jersey?

14. POLITICS Mi-Ling wants to mail at least 850 fliers encouraging voters to vote for theupcoming school levy. She has five days to get them all in the mail.

a. Write an inequality to represent how many fliers Mi-Ling must mail every day.

b. How many fliers should Mi-Ling mail each day?

43210 9 10876

76543 4140393837

�98 �96 �95 �94�97 �15 �14 �13 �12 �11

6261605958 �27 �26 �25 �24 �23

�218 �217 �216 �215 �214 1615141312

�48 �47 �46�50 �495 6432

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Reading to Learn MathematicsSolving Inequalities by Multiplying or Dividing

NAME ______________________________________________ DATE ____________ PERIOD _____

7-57-5

How are inequalities used in studying space?


a. Divide each side of the inequality 300 � 50 by 2. Is the inequality stilltrue? Explain by using an inequality.

b. Would the weight of 5 astronauts be greater on Pluto or on Earth?Explain by using an inequality.

Pre-Activity

Reading the Lesson

1. Describe the Multiplication Property of Inequality for both positive and negative numbers and give an example of a problem for each type of number.

2. Describe the Division Property of Inequality for both positive and negative numbers andgive an example of a problem for each type of number.


3. In the boxes below, write examples of inequalities in which the sign does and does notreverse. Write at least three examples in each box.

Inequalities in Whichthe Sign Does Not Reverse

Inequalities in Whichthe Sign Reverses

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

7-57-5


Hidden WordIn each group of five inequalities, only two have the same solution set. For eachgroup, write the solution of each inequality and then circle the letters of the twoinequalities having the same solution set. After completing all four groups, use thecircled letters to form a one-word answer to the question at the bottom of the page.

GROUP 1

E. 3x� 30 B. �3x � �30 F. �30 � 3x D. �30 � �3x D. �3x � 30

GROUP 2

M. �5x

� � �2 N. ��

5x� � 2 W. �

�

x5� � �2 R. �

�

2x� � �5 R. �

�

5x� � �2

GROUP 3

Q. �32x� � 0 K. 0 � �12x L. �

�

x1� � 0 L. 0.73x � 0 A. 0 � �912x

GROUP 4

L. 200 � 0.05x A. 0.05x � 20 D. �15

�x � 20 E. 200 � 5x E. �0x.1� � 4000

Unscramble the circled letters to find the name of the first of the original 13colonies to ratify the U.S. Constitution.

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Some inequalities require more than one step to solve. For such inequalities, undo the operations inreverse order, just as in solving multi-step equations.

Remember to reverse the inequality symbol when multiplying or dividing each side of the inequality by a negative number.

Solve 12 � 2x � 24 � 2x and check your solution. Graph the solutionon a number line.

12 � 2x � 24 � 2x Write the inequality.

12 � 2x � 2x � 24 � 2x � 2x Subtract 2x from each side.

12 � 4x � 24 Simplify.

12 � 12 � 4x � 24 � 12 Subtract 12 from each side.

�4x � 12 Simplify.

��

�

44x

� � ��

124� Divide each side by –4 and reverse the symbol.

x � �3 Simplify.

CHECK

12 � 2x � 24 � 2x Try –4, a number less than –3.

12 � 2(�4) � 24 � 2(�4) Replace x with –4.

12 � 8 � 24 � 8 Simplify.

20 � 16 � The solution checks.

Graph the solution x � �3.

Study Guide and InterventionSolving Multi-Step Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

ExampleExample

7-67-6

ExercisesExercises

�3 �2 �1�4�5

If the inequality contains parentheses, use the Distributive Property to begin simplifying the inequality.

Solve each inequality and check your solution. Graph the solution on a number line.1. 5c � 9 � �11 2. 8 � 4 p � 20

3. c � 5 � 4c � 1 4. 18 � 2n � 6

5. 3(d � 2) � �15 6. �b3

� � 9 � 8

�4 �3 �2�5�6 �5 �4 �3 �2 �1

43210 7 8654

�9 �8 �7 �6 �5 �3�4�5 �2 �1

Skills PracticeSolving Multi-Step Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

7-67-6


Solve each inequality and check your solution. Graph the solution on a number line.

1. 3x � 9 � 18 2. 5 � 2c � �9

3. 4x � 3 � 2 � x 4. 3(n � 2) � 24

5. 11 � 2b � 3(2 � b) 6. �m3

� � 5 � 2

7. �12

� (8 � x) � 6 8. �4c

� � 7 � 5

9. y � 3 � 5y � 1 10. 20 � 2n � 26

11. �13

� (x � 6) � 2 12. 5 � 2k � 15

13. �2(3 � t) � �8 14. �n4

� �9 � 5

15. Two times a number less 4 is greater than the same number plus 6. For what numberor numbers is this true?

16. One-half of the sum of a number and 4 is less than 14. What is the number?

17. FISHING Benjamin wants to go fishing on the lake. A boat rents for $12 per hour and arod and reel rent for $20 per day. If he wants to spend no more than $80, how manyhours can he spend fishing in the boat?

18. ENTERTAINING Deena is inviting 10 friends to a party. If she wants to spend no morethan $120 on her guests, and dinner for each guest costs $8, what is the most can shespend on party favors for each person?

54321 �9 �8 �7 �6 �5

�1 0 1 2 3 54 6 7 8

10�3 �2 �1�11 �10 �9 �8 �7

�6 �5 �4 �3 �2 �10 �9 �8 �7 �6

10�3 �2 �1 �5 �4 �3 �2 �1

1413121110 �5 �4 �3�6�7

3210�1 5857565554

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PracticeSolving Multi-Step Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

7-67-6

Solve each inequality and check your solution. Then, graph the solution on anumber line.

1. 2x � 12 � �12 2. 6 � 2p � 16

3. 5 � 4k � 21 4. 3(d � 2) � 6

5. �m2� � 7 � 4 6. 0.5c � 2 � 4.5

7. �23

�(12 � x) � 4 8. �12

�(8 � c) � 7.5

9. �3c

� � 7 � 5�12

� 10. 7 � 2p � �14

11. �3(x � 3) � 7.5 12. 5 � 3c � c � 17

13. 2(n � 5) � �7 14. �18

2�n� � 6

15. Two times a number less 10 is greater than five times the same number plus 2. Forwhat number or numbers is this true?

16. One-half of the sum of a number and 12 is less than 27. What is the number?

17. STATE FAIR Admission to the state fair costs $5 and each ride costs $0.75. If Ahmedwants to spend no more than $14 at the fair, how many rides can he ride?

18. GIFTS Yuko wants to buy teddy bears that cost $8.50 each for her eight nieces andnephews. She would like to get a hat for each teddy bear, also. If Yuko wants to spendno more than $94, how much can she spend on each hat?

�14 �13 �12 �11 �10 3 4 5 6 7

�6 �5 �4 �3 �2 210�2 �1

2423222120 1514131211

87654 �5�6�7�8�9

�2�3�4�5�6 �9�10�11�12�13

�4�5�6�7�8 �1�2�3�4�5

0 1 2 3�1 54 6 7 8

Reading to Learn MathematicsSolving Multi-Step Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

7-67-6


How are multi-step inequalities used in backpacking?


a. Write an inequality that represents the relationship between bodyweight and a safe total backpack and contents weight.

b. Suppose you weigh 120 pounds and your empty backpack weighs 5 pounds. Write an inequality that represents the maximum weight youcan safely carry in the backpack.

Pre-Activity

Reading the Lesson

Fill in the blank with the term or phrase that best completes each statement.

1. Solving multi-step inequalities is much like solving multi-step .

2. To solve a multi-step inequality, you should work to undo the operations.

3. The first step in solving an inequality that contains parentheses is to.

4. Remember to the inequality symbol when multiplying or dividing both sidesof the inequality by a negative number.

5. To check the solution x � 14, you should try a number than 14 in the original inequality.


6. Fill in the flow chart for solving an inequality such as �4(d � 2) ≥ �8d � 32 using the steps listed below. Write the letter of the correct step in the appropriate box on the flow chart.

a. Multiply or divide both sides by the coefficient of the variable

b. Use the Distributive Property

c. Add or subtract a term with the variable from both sides

d. Reverse the inequality sign if necessary

e. Add or subtract a constant term from both sides

Simplify

Simplify

Simplify

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Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

7-67-6

Conditional and Unconditional InequalitiesWhen the replacement set is the set of real numbers, the inequality 2x � 16 is called a conditional inequality because it is true for at least one but not all values of the replacement set. Other examples of conditional inequalities are x � 5 � 8 and 2y � 6 � 10.

If the replacement set is the set of real numbers, x � 5 � x is true for every element of the replacement set. Such an inequality is called an unconditional inequality. Other examples of unconditional inequalities are 2x � 9 � 2x and x � 7 � x.

Solve each inequality. Then determine whether each inequality is conditional or unconditional.

1. x � 2 � 4 2. 3x � 2 � 2x � 4

3. 4x � 5 � 4x 4. 2(3x � 5) � 6x � 5

5. 7y � 4 � 6 � 2y 6. 8y � 3y � 5y � 10

7. 5x � 10 � 2(3x � 4) 8. x � 7 � x

9. 2c � 5 � 8 � 2c 10. 6x � 3x � 1 � 8x � x

11. 2x � 3x � 4x � 1 12. 7x � x � 10 � 8x

13. x � 8 � 8 14. 8x � 5(2x � 4)

Chapter 7 Test, Form 1

NAME DATE PERIOD

SCORE


Ass

essm

ent

Write the letter for the correct answer in the blank at the right of each question.

For Questions 1–7, solve each equation.

1. 2m � 2 � 4mA. 2 B. 0 C. �2 D. 1 1.

2. 8 � 3x � 29 � 2xA. 4.2 B. 21 C. �7.2 D. 0 2.

3. 16p � 7 � 2p � 7A. �2 B. 1 C. 2 D. �1 3.

4. 2(r � 5) � 22r

A. �2 B. �12� C. all numbers D. � 4.

5. 15 � h � 4 � hA. 0 B. �1 C. all numbers D. � 5.

6. 2(9s � 3) � 6(3s � 1)A. 0 B. 6 C. all numbers D. � 6.

7. 7d � 2 � 4(d � 1)A. 2 B. �1 C. all numbers D. � 7.

8. Twice a number is 4 more than the number. Choose the equation to find the unknown number, then solve.A. 2x � 4 � x; x � �4 B. 2x � x � 4; x � �

43�

C. 2x � x � 4; x � 4 D. 2x � x � 4; x � �2 8.

For Questions 9 and 10, write an inequality for each sentence.

9. A number minus 14 is more than 35.A. 14 � n � 35 B. n � 14 � 35 C. n � 14 � 35 D. n � 14 � 35 9.

10. Six times a number is at most 91.A. 6k 91 B. 6k � 91 C. 6k � 91 D. 6k � 91 10.

11. If h � 2,which word describes the inequality 6h � 9 � 20?A. open B. true C. false D. addition 11.

12. Choose the inequality whose solution is graphed at the right.A. x � 3 B. x � 3 C. x 3 D. x � 3 12.

13. Charles and Betty spent more than $230 while shopping. Betty spent $138.Choose the inequality that shows what Charles spent.A. c � $108 B. c � $92 C. c � $92 D. c � $92 13.

77

�1�2 0 1 2 4 5 63


Chapter 7 Test, Form 1 (continued)

For Questions 14–23, solve each inequality.

14. x � 4 � 12A. x � 8 B. x � 16 C. x � 8 D. x � 16 14.

15. y � 3 � �16A. y � �13 B. y � �19 C. y � �19 D. y � �13 15.

16. z � 5 � 11A. z � 6 B. z � 16 C. z 16 D. z � �6 16.

17. 6x � 12A. x � �2 B. x � 2 C. x � �6 D. x � 18 17.

18. 4b � �36A. b � �9 B. b � �9 C. b � 9 D. b � 9 18.

19. �5k 20A. k �4 B. k 4 C. k � 4 D. k � �4 19.

20. ��d7�

� 3

A. d � �21 B. d � 21 C. d � �21 D. d � 21 20.

21. 5x � 10 � 20A. x � 6 B. x � 2 C. x � 2 D. x � 6 21.

22. �7p � 5 � �33A. p � �4 B. p � 5.14 C. p � 4 D. p � 5 22.

23. �2x

� � 6 � 9

A. x � �30 B. x � 30 C. x � 30 D. x � �30 23.

24. Twice a number increased by 10 is less than 40. Choose the inequality to find the unknown number. Then solve.A. 2(n � 10) 40; n � 10 B. 2n � 10 � 40; n � 15C. 2(n � 10) � 40; n � 10 D. 2n � 10 � 40; n � 15 24.

25. Choose the inequality whose solution is graphed at the right.A. 8a � 6 � �30 B. 8a � 6 � �30C. �8a � 6 � 30 D. �8a � 6 � �30 25.

Bonus SCHOOL PROJECT Green Valley Middle School is B:selling wrapping paper. For each roll of wrapping paper sold the school receives 45 cents. How many rolls of wrapping paper must be sold to reach their goal of at least $81?

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77

�1�2�3�4�5�6 0 1 2

Chapter 7 Test, Form 2A

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essm

ent



1. 4x � 8 � 3x � 1A. �7 B. 7 C. �9 D. �1 1.

2. 13a � 12 � 8a � 13

A. 5 B. �5 C. �15� D. ��

15� 2.

3. 7a � 4 � 3(a � 9) � 4aA. 3 B. 9 C. all numbers D. � 3.

4. 2(k � 4) � �12�(4k � 16)

A. 0 B. 4 C. all numbers D. � 4.

5. Nine less than five times a number is three more than twice the number.Choose the equation to find the unknown number. Then solve.

A. 5 � 9t � 2t � 2; t � 1 B. 5 � 9t � 3t � 2; t � ��12�

C. 5t � 9 � 2t � 3; t � �4 D. 5t � 9 � 2t � 3; t � 4 5.

6. The perimeter of a rectangle is 150 inches. The length is 3 inches longer than five times the width. Find the length.A. 63 B. 12 C. 36 D. 38 6.


7. The cost of a tank of gas at $1.75 per gallon was more than $30.A. 1.75g � 30 B. 1.75g 30 C. 1.75g � 30 D. 1.75g � 30 7.

8. Cassidy’s allowance plus the $18 she earned babysitting was still less than $30.A. a � 18 � 30 B. a � 18 � 30 C. a � 18 � 30 D. a � 18 30 8.

9. If k � 9, which word describes the sentence 4k � 7 30? A. open B. true C. false D. subtraction 9.

10. Choose the inequality whose solution is graphed below.

A. t � �1 B. t � 1 C. t 1 D. t � 1 10.

�1�2�3�4 0 1 2 43

77


Chapter 7 Test, Form 2A (continued)


11. y � 5 � �8A. y � 13 B. y � �3 C. y � 3 D. y � �13 11.

12. m � 1�23� � 1

A. m � ��23� B. m � �2�

23� C. m � 2�

23� D. m � ��

23� 12.

13. 13y � 39A. y � 27 B. y � 27 C. y � 3 D. y � 3 13.

14. ��3

x.2� � �19

A. x � 60.8 B. x � 5.9 C. x � 60.8 D. x � 5.9 14.

15. ��3t� � 27

A. t � �9 B. t � �81 C. t � �9 D. t � �81 15.

16. �6x � 3 � �21A. x � 4 B. x � 4 C. x � 3 D. x � 3 16.

17. 5 � 0.4s � 30A. s � 62.5 B. s � 62.5 C. s � 12 D. s � 12 17.

18. GOLDFISH The longest recorded life span of a goldfish is 41 years.Suppose you have a goldfish that is 8 years old. Write and solve an inequality to find out how much longer your goldfish could live.A. 8 � y 41; 33 yr B. 8 � y 41; 49 yrC. y � 8 41; 33 yr D. y � 8 41; 49 yr 18.

19. EARNINGS Nichelle earns $7 per hour and gets a 10% commission on the sale price of each item she sells. She wants to work only 10 hours each week, and has a weekly earnings goal of $200. Choose the inequality to find the total sales she must make to reach her goal. Then solve.A. (7)(10) � 1.10s � 200, s � 118.18 B. (7)(10)(0.10)s � 200, s � 28.25C. (7)(10) � 1.10s 200, s � 118.18 D. 7(10) � 0.10s � 200, s � 1300 19.

20. Five times a number decreased by 8 is less than 92. Choose the inequality to find the unknown number. Then solve.A. 5n 8 � 92, n � 147.2 B. 5n � 8 � 92, n � 16.8C. 5n � 8 � 92, n � 20 D. 5n � 8 � 92, n � 20 20.

Bonus Five times the quantity s � 6 equals three times the B:quantity s � 2. What value of s makes this sentence true?

NAME DATE PERIOD

77

Chapter 7 Test, Form 2B

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1. 5x � 11 � 2x � 1A. 6 B. �5 C. 2 D. �4 1.

2. 4z � 23 � 8z � 7A. 3 B. �4 C. 10 D. �10 2.

3. 3(m � 2) � �14�(12m � 24)

A. 0 B. �4 C. all numbers D. � 3.

4. 8a � 3 � 5(a � 7) � 3aA. 0 B. 3 C. all numbers D. � 4.

5. Six less than four times a number is twelve more than twice the number.Choose the equation to find the unknown number. Then solve.A. 6 � 4b � 12 � 2b; b � �1 B. 6 � 4b � 12 � 2b; b � 1C. 4b � 6 � 12 � 2b; b � �9 D. 4b � 6 � 12 � 2b; b � 9 5.

6. The perimeter of a rectangle is 146 inches. The length is 7 inches shorter than three times the width. Find the length.A. 20 in. B. 16.5 in. C. 53 in. D. 56.5 in. 6.


7. The cost of apples at $1.89 per pound was more than $5.A. 1.89p 5 B. 1.89p � 5 C. 1.89p � 5 D. 1.89p � 5 7.

8. The crew of the airplane plus the 37 passengers was at or above the maximum occupancy of 35.A. c � 37 � 35 B. c � 37 � 35 C. c � 37 � 35 D. c � 37 35 8.

9. If p � 5, which word describes the inequality 5p � 7 � 25?A. open B. true C. false D. addition 9.

10. Choose the inequality whose solution is graphed below.

A. s � �3 B. s � �3 C. s � �3 D. s �3 10.

�6�5�4�3�2�1 0 1 2

77


Chapter 7 Test, Form 2B (continued)


11. d � 5 �11A. d � �16 B. d � �16 C. d �6 D. d � �6 11.

12. t � �78� � 2

A. t � 1�18� B. t � 2�

78� C. t � 1�

18� D. t 2�

78� 12.

13. 15x � 60A. x � 45 B. x � 45 C. x � 900 D. x � 4 13.

14. ��

a4.1� � �16

A. a � 3.9 B. a � 3.9 C. a � 65.6 D. a � 65.6 14.

15. ��5s

� � 35

A. s � �7 B. s � �7 C. s � �175 D. s � �175 15.

16. �4x

� � 4 � 16

A. x � 80 B. x � �80 C. x � 5 D. x � �5 16.

17. 7 � 0.6t � 25A. t � 18 B. t � 10.8 C. t � 30 D. t � 30 17.

18. CATS Many cats can live up to 20 years. Suppose you have a cat that is 11 years old. Write and solve an equality to find out how much longer your cat might live.A. y � 11 20; 31 yr B. 11 � y 20; 9 yrC. y � 11 20; 31 yr D. 11 � y 20; 31 yr 18.

19. EARNINGS Maria earns $8 per hour and gets a commission of 5% on the sale price of each item she sells. She wants to work only 15 hours each week, and earn at least $200 each week. Choose the inequality to find the dollar value of the sales Maria must make to reach her goal. Then solve.A. (8)(15) � 0.50s 200, s 1600 B. (8)(15) � 0.05s � 200, s � 1600C. (8)(15)(0.5)s 200, s 60 D. (8)(15)(0.5)s � 200, s � 60 19.

20. Twice the sum of a number and 5 is less than 40. Choose the inequality to find the unknown number. Then solve.A. 2(n � 5) � 40, n � 15 B. 2(n � 5) � 40, n � 15C. 2n � 5 � 40, n � 17.5 D. 2n � 5 � 40, n � 22.5 20.

Bonus Three times the quantity a � 4 equals four times the B:quantity a � 1. What value of a makes this sentence true?

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77

Chapter 7 Test, Form 2C



1. 5a � 10 � 4a � 8 1.

2. 9b � 12b � 6 2.

3. 8f � 14 � (�12f) � 6 3.

4. 4y � 36 � 2y � 42 4.

5. 3(x � 4) � 18x 5.

6. 5(y � 8) � 3(y � 24) 6.

7. 2(5n � 3) � 8n � 2(n � 3) 7.

8. 9n � 3 � 7(n � 3) � 2n 8.

9. Define a variable and write an equation to find the number. 9.Then solve.Eight times a number is twelve times the number minus four.

10. Find the dimensions of the rectangle. 10.The perimeter is given.

11. Four times the sum of three consecutive 11.integers is 180. What are the integers?

12. READING During the summer, Cecile read twice as many 12.books as Kami. Laura read three times as many books as Kami. Gigi read the same number of books as Cecile,Laura, and Kami combined. If Gigi read 30 books, how many books did each of the girls read?


13. SAVINGS Chondra made a $65 withdrawal from her 13.savings account which now has a balance less than $500.

14. Craig’s earnings at $12 per hour were more than $240. 14.

15. For x � 6, state whether �4x5� � 9 is true or false. 15.

NAME DATE PERIOD

SCORE 77

Ass

essm

ent

w

2w + 15

P = 210 ft


Chapter 7 Test, Form 2C (continued)

Graph each inequality on the number line.

16. a � 5 16.

17. m 14 17.

18. y �28 18.


19. b � 4 6.2 19.

20. d � 27 � 14 20.

21. f � (�13) �13 21.

22. 4a � 36 22.

23. �7x

� 12 23.

24. �12y � �108 24.

25. ��z5�

� 50 25.

26. 3.7c � �33.3 26.

27. 6y � 8 � 32 27.

28. ��12�m � 5 � 25 28.

29. �2(f � 2) � 18 29.

30. Francisco needs at least 86 points to pass Ellen’s score. 30.Ellen has 631 points. How many points does Francisco have?

31. The sum of an integer and the next greater integer is at 31.most 13. Write an inequality to find the lesser integer.Then solve for the lesser integer.

32. ORANGES Donna has picked 38 oranges. How many bags 32.can she fill if she puts at least 6 oranges in each bag?

33. If 8 times an integer is decreased by 12, the result is less 33.than 44. Find the integer.

Bonus Give an example of an equation that has no solution. B:

�27�28�29 �26 �25 �24

12111098 13 14 1615

�1�2 0 1 2 4 5 63

NAME DATE PERIOD

77

Chapter 7 Test, Form 2D



1. h � 9 � 2h � 1 1.

2. 7b � 2b � 10 2.

3. 2x � 10 � 17x 3.

4. 7d � 4 � 10d � 23 4.

5. 2(x � 5) � 20x 5.

6. 4(y � 9) � 2(y � 21) 6.

7. 3(2n � 3) � 9n � 3(n � 3) 7.

8. 12n � 3 � 7(n � 4) � 5n 8.

9. Define a variable and write an equation to find the number. 9.Then solve.Nine times a number is one more than ten times the number.

10. Find the dimensions of the rectangle. 10.The perimeter is given.

11. Four times the sum of three consecutive integers is 156. 11.What are the integers?

12. READING During the summer, Bernardo read three times 12.as many books as Kyle. Elan read twice as many books as Kyle. Nate read the same number of books as Bernardo,Kyle, and Elan combined. If Nate read 36 books, how many books did each of the other boys read?


13. SAVINGS Shay made an $80 deposit into her savings 13.account which now has a balance that is at least $600.

14. Shaun’s earnings at $12 per hour were less than $150. 14.

15. For a � 6, state whether �5a1� � 9 is true or false. 15.

NAME DATE PERIOD

SCORE 77

Ass

essm

ent

w

3w – 15

P = 250 ft


Chapter 7 Test, Form 2D (continued)

Graph each inequality on the number line.

16. a � 4 16.

17. m 12 17.

18. y �26 18.


19. b � 4 � 4.7 19.

20. d � 50 � 23 20.

21. f � (�8) � 8 21.

22. 7a � 56 22.

23. �9x

� 11 23.

24. � 14y �210 24.

25. ��z4�

� 36 25.

26. 4.2c � �33.6 26.

27. 7y � 5 � 30 27.

28. ��12�m � 3 � 23 28.

29. �3(x � 2) � 12 29.

30. Pascal needs at least 93 points to pass Matthew’s score. 30.Matthew has 684 points. How many points does Pascal have?

31. The sum of an integer and the next greater integer is at 31.most 15. Write an inequality to find the lesser integer. Then solve for the lesser integer.

32. APPLES Dave has picked 68 apples. How many bags can 32.he fill if he puts at least 9 apples in each bag?

33. If 5 times an integer is decreased by 17, the result is greater 33.than 63. Find the integer.

Bonus Give an example of an equation that is an identity. B:

�27�28 �26 �25 �23�24

12111098 13 14 1615

�1�2 0 1 2 4 5 63

NAME DATE PERIOD

77

Chapter 7 Test, Form 3


For Questions 1–6, solve each equation. Check your solution.

1. 5.7d � 3.2d � 8 1.

2. �35�x � 4 � �

25�x � 6 2.

3. �a

1�0

7� � �

a �8

2� 3.

4. �4(2b � 9) � �13�(�24b � 108) 4.

5. �0a.6�

� 3a � 2 5.

6. �23�d � 4 � �

13�(2d � 7) 6.

7. VOLCANOES Deception Island in Antarctica and Kilauea 7.in Hawaii are two volcanoes that erupted in the twentieth century. The height of Deception Island is 2119 feet shorter than the height of Kilauea. The height of Kilauea is 229 feet more than two times the height of Deception Island. Find the height of Kilauea. Source: World Almanac

8. DECORATING A roll of wallpaper covers 70 square feet. 8.Suppose a rectangular room measures 10 feet long by 12 feet wide by 8 feet high and has two windows and two doors.How many whole rolls of wallpaper are needed to wallpaper the room? Subtract 15 square feet for each window and door.

9. Write an inequality for the graph shown below. 9.

10. Graph n � �12 on a number line. 10.

11. Find a value for x that satisfies the inequality 0.7 � x � 0.81. 11.

12. REAL ESTATE In Grapevine, TX, between 2000 and 2001, 12.the average home price rose from $176,000 to $197,000.During the same time, the average home price in Southlake rose from $405,000 to $412,000. Write an inequality that compares the increases in the average home price for the two cities. Source: Northeast Tarrant County Board of Realtors

�10�20 0 10 20 4030

NAME DATE PERIOD

SCORE 77

Ass

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ent


Chapter 7 Test, Form 3 (continued)

13. Describe the numbers that are represented by the graph 13.below.

14. The sum of an integer and the next greater integer is at 14.least 27. Find the lesser integer.

15. Solve 20 � x � (�21). 15.

16. Colin wants to spend no more than $1250 on his trip. The 16.airfare is $439. How much can Colin spend on other things?

17. Solve ��56� � r � �

23�. 17.


18. �3s

� � 7.1 18.

19. �4.5t �67.5 19.

20. 0 �16x 20.

21. ��14�k � 18 21.

22. �23�x � 7 � 15 22.

23. 23 � ��w2�

71 23.

24. �2(y

8� 1)� �

y �5

4� 24.

25. SCHOOL PROJECT The English department at a high 25.school is selling a collection of poems written by seniors for $8. The cost for printing the book is $300 for the design plus $3.00 per book. If they print 600 books, how many do they have to sell to make at least $2000?

Bonus COMPUTER GAME A computer game lets you build B:your own amusement park. Suppose it costs you $25,000 a day to run the park. Assume the average daily attendance is 1250 people. How much should you charge for admission if you want to make a profit of at least $30,000 for a 30-day month? Write an inequality that represents this situation and solve.

�1�2�3�4 0 1 2 43

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77

Chapter 7 Open-Ended Assessment


Demonstrate your knowledge by giving a clear, concise solutionto each problem. Be sure to include all relevant drawings andjustify your answers. You may show your solution in more thanone way or investigate beyond the requirements of the problems.

1. Make up a problem that can be solved by using the inequality$18.00 � 2p � $6.00. Then solve the inequality and graph it on anumber line. What does the solution represent?

2. Make up a problem that can be solved by using the equation$2.43 � $15 � 3x. Then solve the equation. What does the answerrepresent?

3. At an office supply store, a box of 60 pens contains pens of fourdifferent colors. It contains five times as many red pens as blackpens, and four more black pens than green pens. The number ofred, green, and black pens combined is three times the number ofblue pens. How many pens of each color are in the box?

4. Mr. Rodriguez needs to keep the weight of a package he issending to his sister and three children under 4 pounds.

He wishes to send three identical calculators and a 1�34�-pound

chess set.a. Write an inequality that describes the situation.b. What does the variable represent?c. Solve the inequality.d. What does the solution to the inequality represent?

NAME DATE PERIOD

SCORE 77

Ass

essm

ent


Chapter 7 Vocabulary Test/Review

Write the letter of the term that best matches each statement or phrase.

1. 2 � 2 � x � 10 � 2

2. the solution when 3 � �2

3. at least

4. at most

5. 3 � �3x

� 3 � 4

6. x � 2 � 2 � 10 � 2

7. is greater than

8. is less than

9. 6 � 6 or x � x

10. ��

22x

� � ��62�

In your own words—Define each term.

11. inequality

12. identity

identity inequality null or empty set

NAME DATE PERIOD

SCORE 77

a. �

b. �

c.

d. �

e. Addition Property of Inequality

f. Subtraction Property of Inequality

g. Multiplication Property of Inequality

h. Division Property of Inequality

i. null or empty set

j. identity

Ass

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ent

Chapter 7 Quiz (Lessons 7–1 and 7–2)

77



1. 5n � 12 � 3n 2. 7x � 4 � 3x � 16

3. 3n � 9 � 7n � 15 4. 2.5d � 1 � 3d � 4

5. 2(x � 3) � 8 6. 4(y � 7) � 2(2y � 41)

7. 7(b � 3) � 4 � 25 � 7b 8. �14�(6n � 3) � 4n � 1

9. Define a variable and write an equation to find the number.Then solve.Three times a number is 36 less than five times the number.

10. GEOMETRY The perimeter of a rectangle is 44 inches.Find the dimensions if the width is two inches longer than three times the length. Then find the area of the rectangle.

NAME DATE PERIOD

SCORE

Chapter 7 Quiz (Lesson 7–3)


1. Six less than a number is at most 9. 1.

2. Twice a number is at least 12. 2.

3. A number increased by 7 is more than 19. 3.

4. After a $30 withdrawal, Kevin had less than $250 in his 4.savings account.

5. CAVES A spelunker descended 90 vertical feet into a 5.cavern but remained above the water table at �135 feet.

For the given value, state whether the inequality is trueor false.

6. c � 7 10, c � 17 7. �6b � 27, b � �5

For Questions 8 and 9, graph each inequality on a number line.

8. y 1 9. �4 � z

10. Write the inequality for the graph 10.shown at the right. �1�2�3�4�5�6 0 1 2

NAME DATE PERIOD

SCORE 77

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

6.

7.

8.

9.�1�2�3�4�5�6 0 1 2

�1�2�3�4 0 1 2 43



1. �15 � t � 7 1.

2. 6p � �48 2.

3. ��x6�

� �15 3.

4. Solve x � 5 � 8, and graph the solution on the number line. 4.

5. Standardized Test Practice Toby earns $15 for each lawn he mows. Which inequality can be used to find out how many lawns he must mow in a week to earn at least $135.A. 15m � 135 B. 15m 135C. 15m � 135 D. 15m � 135 5.

�1�2 0 1 2 4 5 63

Chapter 7 Quiz (Lesson 7–6)

Solve each inequality. Graph the solution on a number line.

1. 5x � 15 � 2x 1.

2. 13 � 8x 53 2.

3. �2y

� � 5 � 8 3.

4. �4z � 8 � �27 � z 4.

5. 3(5 � x) 18 5.

�1�2�3�4 0 1 2 43

65432 7 8 109

65432 7 8 109

�7�6�5�4�3�2�1�8�9

�7�6�5�4�3�2�1�8�9

NAME DATE PERIOD

SCORE

Chapter 7 Quiz (Lessons 7–4 and 7–5)

77

NAME DATE PERIOD

SCORE

77

Chapter 7 Mid-Chapter Test (Lessons 7–1 through 7–4)




1. t � 4 � 5tA. 1 B. �1 C. 4 D. �4 1.

2. 4(3b � 7) � 64A. 4 B. �4 C. �3 D. 3 2.

3. 9(x � 2) � 3 � 15 � 9xA. all numbers B. no solutionC. 0 D. 3 3.

4. Write an inequality for the graph shown below.

A. y � �7 B. y �7 C. y � �7 D. y � �7 4.

5. For z � �3, which word describes the inequality �4 � z � 1?A. open B. trueC. false D. subtraction 5.


6. 12p � 7 � 3p � 11 6.

7. 5(3s � 2) � 3s � 14 7.

8. 3(m � 2) � 6m � 3(m � 7) 8.

9. Write an inequality for a savings account balance increased 9.by $150 is now more than $825.

10. Graph t � 4 on a number line. 10.�1�2 0 1 2 4 5 63

Part II

�7�6�5�4�3�2�8�9�10

Part I

NAME DATE PERIOD

SCORE 77

Ass

essm

ent


Chapter 7 Cumulative Review (Chapters 1–7)

For Questions 1 and 2, simplify each expression.(Lessons 2-4 and 3-2)

1. �6(�4a)(�2b) 1.

2. 4t � 4 � 11 � t 2.

3. Determine whether 350 is divisible by 2, 3, 5, 6, or 10. 3.(Lesson 4-1)

4. Find 3�13� 2�

34�. Write in simplest form. (Lesson 5-4) 4.

5. Find the least common denominator (LCD) of �161a2b� and �24

5ab�. 5.

(Lesson 5-6)

6. Find 3�56� � 5�

23�. Write in simplest form. (Lesson 5-7) 6.

7. What is the scale factor of the scale �12� inch � 2 feet? 7.

(Lesson 6-3)

8. Express �176�

as a percent. (Lesson 6-4) 8.

9. Suppose a place setting of china is on sale at a 15% discount. 9.If it normally sells for $129.99, what is the sale price?(Lesson 6-7)

10. Ten cards are numbered 1 through 10, and one card is 10.chosen at random. What is the probability that the card has a number greater than or equal to 4? (Lesson 6-9)

11. Solve 5(a � 3) � 4 � 3a � 27. (Lesson 7-1) 11.

12. Belinda has more than two times as many pairs of shoes as 12.Georgia and more than twice as many as Nina. If both Georgia and Nina have at least 5 pairs each, how many pairs of shoes does Belinda have? (Lesson 7-2)

13. Five times the sum of a number and 15 is greater than 37. 13.What is the number? (Lesson 7-3)

Solve each inequality.(Lessons 7-4 through 7-6)

14. x � �35� � 4 15. �

�k10� � 4 16. �3

x� � 5 � 3

NAME DATE PERIOD

77

14.

15.

16.

Standardized Test Practice (Chapters 1–7)


1. If the value of y � 7 is 18, what is the value of y? (Lesson 1-3)

A. 35 B. 11 C. 25 D. 7 1.

2. Evaluate x � y � z if x � 3, y � 2, and z � 4. (Lesson 2-3)

E. �3 F. 1 G. 9 H. 5 2.

3. Solve ��x7�

� �196. (Lesson 3-4)

A. 1372 B. 28 C. �189 D. �28 3.

4. Write 8b � 20 in factored form. (Lesson 4-4)

E. 4(b � 5) F. 8(b � 5) G. 4(2b � 5) H. 2(4b � 10) 4.

5. Find the least common multiple (LCM) of 16st2u and 8s2u2.(Lesson 5-6)

A. 8stu B. 16s2t2u2 C. 128s3t2u3 D. 2st2u2 5.

6. Find the sum of 3�45� and 2�1

70�

. Write in simplest form. (Lesson 5-7)

E. 6�150�

F. 5�12� G. 5�1

151� H. 6�

12� 6.

7. How much less is �176�

than 2�14�? (Lesson 5-7)

A. 1�12� B. 1�

34� C. 1�

1136�

D. �1156�

7.

8. Which scale has a scale factor of �418�

? (Lesson 6-3)

E. 2 in. � 36 ft F. 3 in. � 12 ft G. 2 in. � 6 ft H. 3 in. � 6 ft 8.

9. Amelia paid $4.79 for 2 gallons of juice. What was the price per quart of juice? (Lesson 6-1)

A. $2.40 B. $1.20 C. $0.40 D. $0.60 9.

10. Choose the best estimate for 48% of 438. (Lesson 6-6)

E. 240 F. 175 G. 220 H. 260 10.

11. The graph shows the results of a survey on voting preferences. Out of a group of 500 voters, how many would you expect to say they prefer to vote on the Internet?(Lesson 6-9)

A. 120 B. 24C. 200 D. 115 11. DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

NAME DATE PERIOD

77

Ass

essm

ent

Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

Voting Preference

In booths50%

OnInternet

24%

By mail23%

Other3%


Standardized Test Practice (continued)

12. Solve 4m � 6 � 8m � 2. (Lesson 7-1)

E. �2 F. �1 G. 1 H. 2 12.

13. Write the inequality for the graph.(Lesson 7-3)

A. a � 3 B. b � 3 C. c 3 D. d � 3 13.

14. Solve x � 6.9 � �9.1. (Lesson 7-4)

E. x � 2.2 F. x � �2.2 G. x � �16 H. x �2.2 14.

15. Solve ��m

6� �30. (Lesson 7-5)

A. m � 30 B. m 180 C. m � 30 D. m � 180 15.

16. Which inequality represents six less than three times a number is more than eighteen? (Lesson 7-6)

E. (6 � 3)n � 18 F. 3n � 6 � 18 G. 3n � 6 � 18 H. 6n � 3 � 18 16.

17. Find the number of miles traveled by driving at 17. 18.50 miles per hour for 4�

12� hours. (Lesson 3-7)

18. The perimeter of a rectangle is 52 feet. The length is 2 feet shorter than three times the width. Find the area of the rectangle in squarefeet. (Lesson 7-2)

19. A new mountain bike is worth only about 0.70 of its value 19.from the previous year during the first four years after it is purchased. Approximately how much will a $900 bicycle be worth in 1, 2, 3, and 4 years? Round your answers to the nearest whole dollar. (Lesson 5-10)

20. The number of baskets scored by a 20.high school basketball team are shown in the table. Write an inequality that represents the number of baskets they must score in their sixth game to have an average of more than 40 baskets per game. (Lesson 7-6)

Part 3: Short Response

Instructions: Write your answer in the blank at the right of each question.

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

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.

HGFE

DCBA

HGFE

DCBA

HGFE

NAME DATE PERIOD

77

NAME DATE PERIOD

�1�2 0 1 2 4 5 63

Game Baskets1 29

2 43

3 36

4 46

5 38

Standardized Test PracticeStudent Record Sheet (Use with pages 364–365 of the Student Edition.)

© Glencoe/McGraw-Hill A1 Glencoe Pre-Algebra

NAME DATE PERIOD

77

An

swer

s

Select the best answer from the choices given and fill in the corresponding oval.

1 4 7 9

2 5 8 10

3 6

Solve the problem and write your answer in the blank.

For Questions 11, 14, 17, 20, and 22, also enter your answer by writing eachnumber or symbol in a box. Then fill in the corresponding oval for that number or symbol.

11 (grid in) 11 14 17

12

13

14 (grid in)

15

16 20 22

17 (grid in)

18

19

20 (grid in)

21

22 (grid in)

Record your answers for Questions 23–24 on the back of this paper.

Part 2 Short Response/Grid InPart 2 Short Response/Grid In

Part 1 Multiple ChoicePart 1 Multiple Choice

Part 3 Open EndedPart 3 Open Ended

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Skills Practice

So

lvin

g E

qu

atio

ns

wit

h V

aria

ble

s o

n E

ach

Sid

e

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

7-1

7-1

Sol

ve e

ach

eq

uat

ion

.Ch

eck

you

r so

luti

on.

1.3x

12 5

5x1

2.n2

12 5

3n�

6

3.2 2

3b5

7b1

12�

14.

4d2

11 5

2d1

79

5.2f1

3 5

11f2

243

6.8y

111

52y

129

3

7.5a

545

12a

158.

17 2

3c5

4c1

32

9.2a

23 5

9a2

10

110

.5b

521

14b

21

11.

9y2

27 5

22y

16

312

.2n

25 5

7n�

1

13.2

s1

3 5

5s1

21�

314

.7 2

4c5

3c1

35�

4

15.

30 2

2n5

4n5

16.

29 1

7d5

5d1

15�

7

17.

16k2

23 5

6k2

131

18.

w2

20 5

6w�

4

19.

33g1

28 5

25g2

12�

520

.6h

234

52

6h1

144

21.

3t1

17 5

t2

3�

1022

.11

j5

6j2

15�

3

23.

c2

2 5

3c1

14�

824

.28

x2

7 5

26x1

56

25.

5m2

6 5

8m1

9�

526

.2

4p2

7 5

5p 1

11�

2

27.2

10 1

3f5

5f1

6�

828

.4

f1

6 5

8f2

145

29.2

7n2

16 5

4n1

17�

1130

.5d

59d

218

4.5

Def

ine

a va

riab

le a

nd

wri

te a

n e

qu

atio

n t

o fi

nd

eac

h n

um

ber

.Th

en s

olve

.

31.

Th

ree

tim

es a

nu

mbe

r eq

ual

s 40

mor

e th

an f

ive

tim

es t

he

nu

mbe

r.W

hat

is

the

nu

mbe

r?3x

�40

�5x

;�

20

32.

A n

um

ber

equ

als

fou

r le

ss t

han

th

ree

tim

es t

he

nu

mbe

r.W

hat

is

the

nu

mbe

r?x�

3x�

4;2

33.

Eig

ht

tim

es a

nu

mbe

r eq

ual

s 24

mor

e th

an t

wo

tim

es t

he

nu

mbe

r.W

hat

is

the

nu

mbe

r?8x

�24

�2x

;4

Sol

ve e

ach

eq

uat

ion

.Ch

eck

you

r so

luti

on.

1.2x

11 5

x1

112.

a1

2 5

5 1

4a3.

7y1

25 5

2yx �

10a��

1y��

5

4.n1

11 5

2n5.

7 2

4c5

3c2

76.

4 2

3b5

6b2

5n�

11c�

2b�

1

7.9d

29 5

3d2

38.

f2

4 5

6f1

269.

22s

13 5

5s1

24d�

1f��

6s��

3

10.

5a2

3 5

8a1

611

.8n

212

52

12n1

812

.7y

18 52

2y2

64a ��

3n�

1y��

8

13.

1 1

3x5

7x2

714

.6a

23 5

4 1

7a15

.3b

21 5

14 1

2bx�

2a��

7b

�15

16.

12c1

18 5

4 1

5c17

.9y

13 5

5y2

1318

.3n

22 5

5n1

12c ��

2y��

4n

��

7

Exercises

Exercises

To s

olve

equ

atio

ns w

ith v

aria

bles

on

each

sid

e, u

se t

he A

dditi

on o

r S

ubtr

actio

n P

rope

rty

of E

qual

ity t

ow

rite

an e

quiv

alen

t eq

uatio

n w

ith t

he v

aria

ble

on o

ne s

ide.

The

n so

lve

the

equa

tion.

12x2

35

4x 1

13W

rite

the

equa

tion.

12x2

4x2

3 5

4x2

4x1

13S

ubtr

act

4xfr

om e

ach

side

.

8x2

3 5

13S

impl

ify.

8x2

3 1

3 5

13 1

3A

dd 3

to

each

sid

e.

8x5

16S

impl

ify.

x5

2M

enta

lly d

ivid

e ea

ch s

ide

by 8

.

To

chec

k yo

ur

solu

tion

,rep

lace

xw

ith

2 i

n t

he

orig

inal

equ

atio

n.

CH

EC

K

12x2

3 5

4x 1

13W

rite

the

equa

tion.

12(2

) 2

3 0

4(2)

113

Rep

lace

xw

ith 2

.

24 2

3 0

8 1

13C

heck

to

see

whe

ther

the

sta

tem

ent

is t

rue.

21 5

21T

he s

tate

men

t is

tru

e.

Example

ExampleSt

udy Guide and Intervention

So

lvin

g E

qu

atio

ns

wit

h V

aria

ble

s o

n E

ach

Sid

e

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

7-1

7-1

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Lesson 7-1

Sol

ve t

he

equ

atio

n 1

2x�

3�

4x�

13.T

hen

ch

eck

you

r so

luti

on.


Answers (Lesson 7-1)

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Reading to Learn Mathematics

So

lvin

g E

qu

atio

ns

wit

h V

aria

ble

s o

n E

ach

Sid

e

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

7-1

7-1

Ho

w is

so

lvin

g e

qu

atio

ns

wit

h v

aria

ble

s o

n e

ach

sid

e lik

eso

lvin

g e

qu

atio

ns

wit

h v

aria

ble

s o

n o

ne

sid

e?

Do

the

acti

vity

at

the

top

of

pag

e 33

0 in

you

r te

xtb

ook

.Wri

te y

our

answ

ers

bel

ow.

a.T

he

two

side

s ba

lan

ce.W

ith

out

look

ing

in a

bag

,how

can

you

de

term

ine

the

nu

mbe

r of

blo

cks

in e

ach

bag

?S

amp

le a

nsw

er:

Rem

ove

on

e b

ag f

rom

eac

h s

ide.

Th

en r

emov

e 3

blo

cks

fro

m e

ach

sid

e.T

her

e m

ust

be

2 b

lock

s in

eac

h b

ag.

b.

Exp

lain

wh

y yo

ur

met

hod

wor

ks.

Rem

ovin

g t

he

sam

e th

ing

fro

m e

ach

sid

e ke

eps

the

scal

e in

bal

ance

.

c.S

upp

ose

xre

pres

ents

th

e n

um

ber

of b

lock

s in

th

e ba

g.W

rite

an

eq

uat

ion

th

at i

s m

odel

ed b

y th

e ba

lan

ce.

2x�

3�

x�

5

d.

Exp

lain

how

you

cou

ld s

olve

th

e eq

uat

ion

.S

ub

trac

t x

fro

m e

ach

sid

e.T

hen

su

btr

act

3 fr

om

eac

h s

ide.

Pre-

Act

ivit

y

Rea

din

g t

he

Less

on

Des

crib

e in

wor

ds

each

ste

p s

how

n f

or s

olvi

ng

the

foll

owin

g eq

uat

ion

.

1.2x

14 5

4x2

8W

rite

th

e eq

uat

ion

.

2.2x

22x

14 5

4x2

2x2

8S

ub

trac

t 2x

fro

m e

ach

sid

e.

3.4 5

2x2

8S

imp

lify.

4.4 1

8 5

2x2

8 1

8A

dd

8 t

o e

ach

sid

e.

5.12

52x

Sim

plif

y.

6.}1 22 }

5}2 2x }

Div

ide

each

sid

e by

2.

7.6 5

xS

imp

lify.

Hel

pin

g Y

ou

Rem

emb

er

8.W

rite

ou

t an

equ

atio

n l

ike

that

sh

own

abo

ve (

2x1

4 5

4x2

8),a

lon

g w

ith

all

th

e st

eps

nee

ded

to s

olve

th

e eq

uat

ion

.Exc

han

ge e

quat

ion

s w

ith

a p

artn

er.T

hen

eac

h o

f yo

u s

hou

ld e

xpla

in v

erba

lly

wh

y ea

ch s

tep

in s

olvi

ng

the

equ

atio

n w

as c

arri

ed o

ut,

for

exam

ple,

“2x

was

su

btra

cted

fro

m e

ach

sid

e to

eli

min

ate

the

vari

able

on

th

e le

ft s

ide.

”S

tud

ents

sh

ou

ld b

e ab

le t

o d

escr

ibe

corr

ectl

y w

hy e

ach

ste

p in

th

e so

luti

on

pro

cess

is n

eces

sary

.

Practice

So

lvin

g E

qu

atio

ns

wit

h V

aria

ble

s o

n E

ach

Sid

e

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

7-1

7-1

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Sol

ve e

ach

eq

uat

ion

.Ch

eck

you

r so

luti

on.

1.3g

212

59g

�2

2.14

m5

18 1

12m

9

3.7c

27 5

4c1

178

4.2

11t5

15 2

6t�

3

5.20

s1

4 5

13s2

10�

26.

22h

216

53h

26�

2

7.27

j2

6 5

14j1

71

8.2

1 1

19w5

11w1

233

9.8 2

p52

12 2

3p�

1010

.9k

226

56k

28

6

11.

28 2

4d5

5d2

175

12.

2y1

7 5

y�

7

13.

11.7

22x

5x

3.9

14.

3b1

4.4 5

2.6 2

6b�

0.2

15.

}3 4}y2

6 5

}1 4}y1

1032

16.

2c1

7.5 5

6.2 2

3c�

0.26

17.

5d2

11 5

2d1

2}1 33 }

or

4 }1 3}

18.

6a2

10 5

2a2

7}3 4}

19.

8n2

6 52

9n1

111

20.

2f2

9 5

14f1

1�

}5 6}

Def

ine

a va

riab

le a

nd

wri

te a

n e

qu

atio

n t

o fi

nd

eac

h n

um

ber

.Th

en s

olve

.

21.

Tw

ice

a n

um

ber

is 6

0 m

ore

than

fiv

e ti

mes

th

e n

um

ber.

Wh

at i

s th

e n

um

ber?

2x�

60�

5x;�

20

22.

Fou

r ti

mes

a n

um

ber

is 2

1 m

ore

than

th

e n

um

ber.

Wh

at i

s th

e n

um

ber?

4x�

21�

x;7

23.

Eig

ht

less

th

an t

hre

e ti

mes

a n

um

ber

equ

als

the

nu

mbe

r.W

hat

is

the

nu

mbe

r?

3x�

8�

x;4

24.

A n

um

ber

equ

als

six

less

th

an f

our

tim

es a

nu

mbe

r.W

hat

is

the

nu

mbe

r?x�

4x�

6;2

25.

TEN

NIS

Th

e ar

ea o

f a

ten

nis

cou

rt i

s 28

08 f

t2,o

r 8

squ

are

feet

mor

e th

an 3

.5 t

imes

th

esi

ze o

f th

e ar

ea o

f a

racq

uet

ball

cou

rt.W

hat

is

the

area

of

a ra

quet

ball

cou

rt?

800

ft2

26.

CEL

LULA

R P

HO

NES

On

e ce

llu

lar

phon

e ca

rrie

r ch

arge

s $2

6.50

a m

onth

plu

s $0

.15

am

inu

te f

or l

ocal

cal

ls.A

not

her

car

rier

ch

arge

s $1

4.50

a m

onth

an

d $0

.25

a m

inu

te f

orlo

cal

call

s.F

or h

ow m

any

min

ute

s is

th

e co

st o

f th

e pl

ans

the

sam

e?12

0 m

inu

tes

Lesson 7-1



An

swer

s

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Equ

atio

ns w

ith g

roup

ing

sym

bols

can

be

solv

ed b

y fir

st u

sing

the

Dis

trib

utiv

e P

rope

rty

to r

emov

e th

egr

oupi

ng s

ymbo

ls.

2(6m

21)

58m

Writ

e th

e eq

uatio

n.

12m2

2 5

8mA

pply

the

Dis

trib

utiv

e P

rope

rty.

12m2

12m2

2 5

8m2

12m

Sub

trac

t 12

mfr

om e

ach

side

.

22 52

4mS

impl

ify.

}2 22 4}5}224 4m }

Div

ide

each

sid

e by

–4.

}1 2}5

mS

impl

ify.

CH

EC

K

2(6m

21)

58m

2 161}1 2} 2

21 2

08(

}1 2} )R

epla

ce m

with

}1 2} .

2(3 2

1) 0

4S

impl

ify.

4 5

4�T

he s

olut

ion

chec

ks.

Som

e eq

uatio

ns h

ave

no s

olut

ion.

The

sol

utio

n se

t is

the

nu

llor

em

pty

set

.Oth

er e

quat

ions

hav

e ev

ery

num

ber

as a

sol

utio

n.S

uch

an e

quat

ion

is c

alle

d an

iden

tity

.

Sol

ve e

ach

eq

uat

ion

.Ch

eck

you

r so

luti

on.

1.8(

g2

3) 5

242.

5(x1

3) 5

253.

7(2c

25)

57

4.2(

3d1

7) 5

5 1

6dg�

6x�

2c�

3Ø

5.2(

s1

11) 5

5(s1

2)6.

7y 2

1 5

2(y1

3) 2

27.

2(f1

3) 2

2 5

8 1

2fs�

4y�

1Ø

8.2(

x2

2) 1

3 5

2x2

19.

1 1

2(b1

6) 5

5(b2

1)10

.2x

25 5

3(x1

3)al

l nu

mb

ers

b�

6x��

14

Study Guide and Intervention

So

lvin

g E

qu

atio

ns

wit

h G

rou

pin

g S

ymb

ols

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

Example

1Example

1

Exercises

Exercises

7-2

7-2

Example

2Example

2

a.2(

x2

1) 5

4 1

2xb

.2

2(x2

1) 5

2 2

2x

22x

22 5

4 1

2x2

2x1

2 5

2 2

2x

2x2

2x2

2 5

4 1

2x2

2x2

2x1

2 2

2 5

2 2

2 2

2x

22 5

42

2x52

2xT

he

solu

tion

set

is

Ø.

x5

xT

he

solu

tion

set

is

all

real

nu

mbe

rs.

Sol

ve t

he

equ

atio

n 2

(6m

�1)

�8m

.Ch

eck

you

r so

luti

on.

Sol

ve e

ach

eq

uat

ion

.

Enrichment

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

7-1

7-1

©G

lenc

oe/M

cGra

w-H

ill37

1G

lenc

oe P

re-A

lgeb

ra

Fra

ctio

nal

Eq

uat

ion

sT

o so

lve

equ

atio

ns

con

tain

ing

frac

tion

s,m

ult

iply

bot

h s

ides

by

the

leas

t co

mm

on

den

omin

ator

.Th

en s

olve

as

usu

al.

Sol

ve}2 5x }

2} 1x 0}

56.

}2 5x }2

} 1x 0}5

6T

he le

ast

com

mon

den

omin

ator

is 1

0.

10 1}2 5x }

2} 1x 0}25

10(6

)

101}2 5x }22

101} 1x 0}25

10(6

)

4x2

x5

10(6

)

3x5

60

}3 3x }5

}6 30 }

x5

20

Sol

ve e

ach

eq

uat

ion

.

1.}3 2x }

2x5

12

2.}3 8x }

5} 3x }1

}4 3}32

3.} 6y }2

} 4y }5

5�

604.

2a1

}a 3}5

}a 4}1

5}1 52 }

5.}x2 3

2}

5}x1 4

1}

116.}x2 2

1}

1}x� 3

2}

51

}1 53 }

7.}x� 5

3}

2}x

11 52}

1}2 3}5

0}1 2}

8.}x1 3

4}

245}x2 4

11 }�

1

9.2

}d 4}1

d5

}1 8}}1 6}

10.}x2 5

7}

125}x

11 08}

2

11.

z1

} 4z }5

142

} 2z }8

12.}y

11 63}

2}y2 6

4}

5}1 3}

5

Example

Example

Lesson 7-1


Answers (Lessons 7-1 and 7-2)

©G

lenc

oe/M

cGra

w-H

ill37

4G

lenc

oe P

re-A

lgeb

ra

Practice

So

lvin

g E

qu

atio

ns

wit

h G

rou

pin

g S

ymb

ols

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

7-2

7-2

Sol

ve e

ach

eq

uat

ion

.Ch

eck

you

r so

luti

on.

1.4(

j2

7) 5

1210

2.5(

2k1

10) 5

40�

1

3.7(

2p1

3) 2

856p

129

24.

7(g2

4) 5

34

}3 7}

5.3(

4c1

5) 5

240.

756.

2(a2

1) 5

3(a1

1)�

5

7.3(

x2

3) 5

5(1.

5 1

x)�

8.25

8.2(

1.5m

13)

53.

5m2

114

9.a2

} 15 0}5

2a2

}3 5}0.

110

.2.

2x2

5 5

2(1.

4x1

3)�

18.3

11.} 0d .2}

53d

12.

11.

0512

.5n

13 5

2(n1

2) 2

3n}1 6}

13.

}2 3} a1

2 5

}1 3} (4

a1

1)2}

1 2}14

.y2

7 5

}1 4} (y1

2)10

15.

5(f1

2) 5

9 1

5fØ

Fin

d t

he

dim

ensi

ons

of e

ach

rec

tan

gle.

Th

e p

erim

eter

is

give

n.

16.

P 5

122

m13

m b

y 48

m

17.

P 5

244

yd35

yd

by

87 y

d

18.

P 5

698

cm16

3 cm

by

186

cm

19.

P 5

86 i

n20

in b

y 23

in

20.

GEO

MET

RYT

he

peri

met

er o

f a

rect

angl

e is

80

feet

.Fin

d th

e di

men

sion

s if

th

e le

ngt

h i

s5

feet

lon

ger

than

fou

r ti

mes

th

e w

idth

.Th

en f

ind

the

area

of

the

rect

angl

e.w�

7 ft

,<�

33 f

t;A�

231

ft2

21.

NU

MB

ER T

HEO

RYF

ive

tim

es t

he

sum

of

thre

e co

nse

cuti

ve i

nte

gers

is

150.

Wh

at a

re t

he

inte

gers

?9,

10,1

1

w

w �

35

w

3w �

18

w

w �

23

w

w �

3

Skills Practice

So

lvin

g E

qu

atio

ns

wit

h G

rou

pin

g S

ymb

ols

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

7-2

7-2

©G

lenc

oe/M

cGra

w-H

ill37

3G

lenc

oe P

re-A

lgeb

ra

Sol

ve e

ach

eq

uat

ion

.Ch

eck

you

r so

luti

on.

1.2(

g2

7) 5

1615

2.5(

x1

2) 5

304

3.3(

2d1

7) 5

393

4.4(

a2

2) 5

3(a1

4)20

5.3(

f1

2) 1

9 5

13 1

5f1

6.2(

x2

4) 5

3(1 1

x)�

11

7.2n

15 5

4(n1

2) 2

n�

38.

4(x1

3) 5

x�

4

9.2(

c2

3) 5

7641

10.

7(x2

2) 5

5(x1

2)12

11.

2(6x

11)

54(

x2

5) 2

2�

312

.4(

2b2

6) 1

11 5

8b2

13al

l nu

mb

ers

13.

6 1

6(2t

21)

53 1

12t

Ø14

.9t

221

53(

t2

7) 1

6tal

l nu

mb

ers

15.

3(4k

114

) 5

10k2

2(k2

7)�

7

Fin

d t

he

dim

ensi

ons

of e

ach

rec

tan

gle.

Th

e p

erim

eter

is

give

n.

16.

P 5

380

m85

m b

y 10

5 m

17.

P 5

640

yd83

yd

by

237

yd

18.

P 5

220

ft50

ft

by 6

0 ft

19.

P 5

380

yd

30 y

d b

y 16

0 yd

20.

P 5

300

m30

m b

y 12

0 m

w

w �

20

w

3w �

12

w

2w �

40

w

5w �

10

w

w �

90

Lesson 7-2



An

swer

s

©G

lenc

oe/M

cGra

w-H

ill37

6G

lenc

oe P

re-A

lgeb

ra

Enrichment

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

7-2

7-2

So

nya

Vas

iliev

na

Kov

ales

kyS

onya

Vas

ilie

vna

Kov

alev

sky

(185

0218

91),

a R

uss

ian

mat

hem

atic

ian

,ach

ieve

d a

good

ed

uca

tion

an

d a

succ

essf

ul

care

er d

espi

te t

he

disa

dvan

tage

at

that

tim

e of

bei

ng

fem

ale.

Dis

cove

r h

er a

ccom

plis

hm

ents

by

wor

kin

g th

e pr

oble

ms

at t

he

bott

om o

f th

e pa

ge.T

hen

if

you

fin

d yo

ur

answ

er i

n t

he

char

t,ci

rcle

th

e fa

ct i

n t

hat

squ

are.

Eac

h c

ircl

ed f

act

is a

tru

est

atem

ent

abou

t K

oval

evsk

y’s

life

.

1.2z

285

1210

2.28

511

x2

53

3.n2

12 5

542

n33

4.3x

18 5

5x2

67

5.6 1

2s5

7}1 2}

6.} 9x }2

3 5

1718

0

7.9 2

(2a1

6) 5

29

68.

x1

6 5

5 2

x�

}1 2}9.

x1

3(2x

21)

54(

2x1

1)�

7

SO

NYA

VA

SIL

IEV

NA

KO

VAL

EV

SK

Y (

1850

–189

1)

She

was

den

ied

aned

ucat

ion

in R

ussi

a.

Son

ya w

as a

Rus

sian

mat

hem

atic

ian

and

phys

icis

t.

She

bec

ame

a Le

ctur

er a

ndla

ter

Pro

fess

or o

f Hig

her

Mat

hem

atic

s in

Sto

ckho

lm.

She

beg

an h

er fo

rmal

stu

dyat

the

Nav

al A

cade

my

in S

t.P

eter

sbur

g.

She

was

taug

ht p

rivat

ely

by r

enow

ned

mat

hem

atic

ian

Kar

lW

eier

stra

ss in

Ber

lin.

She

wro

te a

pla

y th

at w

aspr

oduc

ed in

Mos

cow

.S

onya

was

bor

n in

Pol

and

and

beca

me

a w

ell-k

now

nm

athe

mat

icia

n an

dno

velis

t.

She

was

mar

ried

just

so

the

Eur

opea

n un

iver

sitie

sw

ould

allo

w h

er to

atte

ndhi

gher

edu

catio

n cl

asse

s.

Upo

n re

ceiv

ing

her

doct

orat

e, s

he w

as o

ffere

dse

vera

l pro

fess

iona

lap

poin

tmen

ts a

ll ov

erE

urop

e.3 10 6

1 2

156

�5

1 4 33

1 2�


So

lvin

g E

qu

atio

ns

wit

h G

rou

pin

g S

ymb

ols

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

7-2

7-2

©G

lenc

oe/M

cGra

w-H

ill37

5G

lenc

oe P

re-A

lgeb

ra

Wh

y is

th

e D

istr

ibu

tive

Pro

per

ty im

po

rtan

t in

so

lvin

g e

qu

atio

ns?

Do

the

acti

vity

at

the

top

of

pag

e 33

4 in

you

r te

xtb

ook

.Wri

te y

our

answ

ers

bel

ow.

a.W

hat

doe

s t

repr

esen

t?th

e ti

me

Josh

tra

vels

b.

Wh

y is

Mar

ia’s

tim

e sh

own

as

t2

1?S

he

left

1 h

late

r th

an J

osh

.

c.W

rite

an

equ

atio

n t

hat

rep

rese

nts

th

e ti

me

wh

en M

aria

cat

ches

up

to J

osh

.(H

int:

Th

ey w

ill

hav

e tr

avel

ed t

he

sam

e di

stan

ce.)

2t�

10(t�

1)

Pre-

Act

ivit

y

Rea

din

g t

he

Less

on

1–2.

See

stu

den

ts’w

ork

.W

rite

a d

efin

itio

n a

nd

giv

e an

exa

mp

le o

f ea

ch n

ew v

ocab

ula

ry w

ord

or

ph

rase

.

3.If

an

equ

atio

n r

esu

lts

in a

sen

ten

ce t

hat

is

nev

er t

rue,

the

solu

tion

set

isth

e n

ull

or

emp

ty s

et.

4.W

hen

an

equ

atio

n r

esu

lts

in a

n i

den

tity

,th

e so

luti

on s

et

isal

l nu

mb

ers

.

5.T

o so

lve

an e

quat

ion

con

tain

ing

grou

pin

g sy

mbo

ls,y

ou m

ust

fir

st u

se

the

Dis

trib

uti

ve P

rop

erty

.

6.F

or a

rec

tan

gle,

two

tim

es t

he

len

gth

plu

s tw

o ti

mes

th

e w

idth

equ

als

the

per

imet

er.

Hel

pin

g Y

ou

Rem

emb

er

7.E

xpla

in i

n a

par

agra

ph w

hy

solv

ing

a ge

omet

ry p

robl

em,l

ike

that

in

Exa

mpl

e 2

in y

our

text

,req

uir

es t

he

use

of

the

Dis

trib

uti

ve P

rope

rty.

You

may

wis

h t

o sk

etch

a f

igu

re a

nd

assi

gn v

alu

es t

o th

e si

des

to a

id y

our

expl

anat

ion

.S

amp

le a

nsw

er:T

o f

ind

th

ep

erim

eter

,yo

u m

ust

ad

d t

og

eth

er t

wo

tim

es t

he

wid

th a

nd

tw

o t

imes

th

ele

ng

th.S

ince

th

e le

ng

th is

giv

en a

s an

exp

ress

ion

,su

ch a

s 3x

�2,

you

mu

st m

ult

iply

th

e ex

pre

ssio

n b

y 2,

2(3x

�2)

,th

eref

ore

req

uir

ing

th

e u

seo

f th

e D

istr

ibu

tive

Pro

per

ty.

Voca

bula

ryD

efin

itio

nE

xam

ple

1.n

ull

or

empt

y se

t

2.id

enti

ty

Lesson 7-2



©G

lenc

oe/M

cGra

w-H

ill37

8G

lenc

oe P

re-A

lgeb

ra

Skills Practice

Ineq

ual

itie

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

__P

ER

IOD

____

_

7-3

7-3

Wri

te a

n i

neq

ual

ity

for

each

sen

ten

ce.

1.M

ore

than

100

,000

fan

s at

ten

ded

the

open

ing

foot

ball

gam

e at

Th

e O

hio

Sta

teU

niv

ersi

ty.

f�10

0,00

0

2.H

er e

arn

ings

at

$16

per

hou

r w

ere

no

mor

e th

an $

96.

16h�

96

3.A

sav

ings

acc

oun

t de

crea

sed

by $

50 i

s n

ow l

ess

than

$74

0.s�

50�

740

4.A

nu

mbe

r in

crea

sed

by 7

is

at l

east

45.

n�

7�

45

For

th

e gi

ven

val

ue,

stat

e w

het

her

eac

h i

neq

ual

ity

is t

rue

or f

alse

.

5.}1 c8 }

,9,

c5

2fa

lse

6.} 5x }$

3,x5

5fa

lse

7.6k

$42

,k5

7tr

ue

8.10

2x,

3,x5

7fa

lse

9.11

1n,

32,n

54

tru

e10

.91

c.

19,c

510

fals

e

Gra

ph

eac

h i

neq

ual

ity

on a

nu

mb

er l

ine.

11.

a,

612

.t $

22

13.

d#

3

14.

b$

1015

.x$2

716

.x .

2

Wri

te t

he

ineq

ual

ity

for

each

gra

ph

.

17.

x�

1018

.x��

2

19.

x��

720

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6

21.

x�

222

.x��

38

78

65

4�

2�

3�

4�

10

45

32

1

1211

109

8�

7�

8�

9�

6�

54

32

10

1211

109

8�

4�

3�

2�

10

�9

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87

65

4

34

21

0�

38�

37�

36�

40�

39

Wri

te a

n i

neq

ual

ity

for

each

sen

ten

ce.

1.Yo

ur

age

is g

reat

er t

han

12

year

s.a�

12

2.A

nu

mbe

r de

crea

sed

by 2

5 is

no

mor

e th

an 6

5.x�

25�

65

3.M

ore

than

$10

00 w

as c

olle

cted

for

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e ch

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Exercises

Exercises

Example

2Example

2

a.x�

8b

.x�

8

Th

e op

en c

ircl

e m

ean

sT

he

clos

ed c

ircl

e m

ean

sth

e n

um

ber

8 is

not

the

nu

mbe

r 8

isin

clu

ded

in t

he

grap

h.

incl

ude

d in

th

e gr

aph

.

A m

athe

mat

ical

sen

tenc

e th

at c

onta

ins

any

of t

he s

ymbo

ls li

sted

bel

ow is

cal

led

an in

equ

alit

y.

a.L

ess

than

70

stu

den

ts a

tten

ded

the

last

dan

ce.

a�

70b

.A

t th

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the

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cost

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mu

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lity

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to h

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tha

t m

ake

the

ineq

ualit

y tr

ue.

Example

1Example

1Study Guide and Intervention

Ineq

ual

itie

s

NA

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____

____

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ATE

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ER

IOD

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7-3

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al t

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tha

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ore

than

• is

no

mor

e th

an•

is n

o le

ss t

han

• ex

ceed

s•

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t m

ost

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67

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Wri

te a

n i

neq

ual

ity

for

each

sen

ten

ce.

Gra

ph

eac

h i

neq

ual

ity

on a

nu

mb

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ine.



An

swer

s

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Ineq

ual

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ME

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ER

IOD

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7-3

7-3

Ho

w c

an in

equ

alit

ies

hel

p y

ou

des

crib

e re

lati

on

ship

s?

Do

the

acti

vity

at

the

top

of

pag

e 34

0 in

you

r te

xtb

ook

.Wri

teyo

ur

answ

ers

bel

ow.

a.N

ame

thre

e ag

es o

f ch

ildr

en w

ho

can

eat

fre

e at

th

e re

stau

ran

t.D

oes

a ch

ild

wh

o is

6 y

ears

old

eat

fre

e?S

amp

le a

ges

:3,

4,5;

no

b.

Nam

e th

ree

hei

ghts

of

chil

dren

wh

o ca

n r

ide

the

ride

at

the

amu

sem

ent

park

.Can

a c

hil

d w

ho

is 4

0 in

ches

tal

l ri

de?

Sam

ple

hei

gh

ts:

42 in

.,43

in.,

44 in

.,n

o

c.N

ame

thre

e sp

eeds

th

at a

re l

egal

.Is

a dr

iver

wh

o is

tra

veli

ng

at

35 m

ph d

rivi

ng

at a

leg

al s

peed

?S

amp

le s

pee

ds:

25 m

ph

,30

mp

h,3

5 m

ph

;ye

s

Pre-

Act

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Rea

din

g t

he

Less

on

Wri

te a

def

init

ion

an

d g

ive

an e

xam

ple

of

the

new

voc

abu

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wor

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For

eac

h o

f th

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llow

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ph

rase

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in

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corr

esp

ond

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ineq

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10.

Th

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ineq

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a.F

ind

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in

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Wri

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no

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f th

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me

size

or

valu

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xpla

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neq

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Sin

ce in

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Voca

bula

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ple

ineq

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See

stu

den

ts’w

ork

.1.

Practice

Ineq

ual

itie

s

NA

ME

____

____

____

____

____

____

____

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____

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ATE

____

____

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ER

IOD

____

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7-3

7-3

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Use

the

Add

ition

and

Sub

trac

tion

Pro

pert

ies

of I

nequ

aliti

es t

o so

lve

ineq

ualit

ies.

Whe

n yo

u ad

d or

su

btra

ct a

num

ber

from

eac

h si

de o

f an

ineq

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he in

equa

lity

rem

ains

tru

e.

Sol

ve 1

2 �

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impl

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an

y n

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ter

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ME

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Example

Example

Exercises

Exercises

7-4

7-4

? ?

Enrichment

NA

ME

____

____

____

____

____

____

____

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ATE

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ER

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7-3

7-3

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Mak

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p a

Pro

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mYo

u h

ave

seen

th

at s

ome

prob

lem

sit

uat

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s ca

n b

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lved

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s an

d op

en

sen

ten

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Usu

ally

in

mat

h,y

ou a

re a

sked

to

solv

e pr

oble

ms.

In t

his

act

ivit

y,yo

u w

ill

bew

riti

ng

the

prob

lem

s.

Use

th

e op

en s

ente

nce

,sto

ry i

dea

,an

d y

our

imag

inat

ion

to

wri

te a

n i

nte

rest

ing

wor

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rob

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.A

nsw

ers

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var

y.S

amp

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nsw

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are

giv

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1.x1

45

83

scor

es o

n a

ch

apte

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stB

etty

ou

tsco

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Sam

by

fou

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the

chap

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test

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3.W

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2.15

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do

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th

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at is

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e m

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end

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rrin

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3.12

1v5

20

a te

am’s

win

/loss

rec

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Th

e B

ulld

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sh

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pla

yed

20

gam

es t

his

sea

son

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hey

hav

e lo

st 1

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wm

any

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peop

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nu

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le w

ere

at a

par

ty.T

hen

10

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ple

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ther

e w

ere

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erth

an 9

peo

ple

left

at

the

par

ty,

ho

w m

any

wer

e th

ere

at t

he

star

t?

5.13

1y�

21

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Bill

will

gra

du

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fro

m

colle

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wh

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e is

at

leas

t 21

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Bill

is 1

3 n

ow

,in

ho

w m

any

year

sw

ill h

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nis

h c

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6.36

1h�

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tem

pera

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p

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by

no

on

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w m

any

deg

rees

had

th

ete

mp

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ure

ris

en b

y n

oo

n?

Lesson 7-3



An

swer

s

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4G

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Practice

So

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Su

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NA

ME

____

____

____

____

____

____

____

____

____

____

____

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ATE

____

____

____

__P

ER

IOD

____

_

7-4

7-4

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So

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NA

ME

____

____

____

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ATE

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ER

IOD

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7-4

7-4

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7-4

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Usi

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d S

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Ho

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qu

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the

acti

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at

the

top

of

pag

e 34

5 in

you

r te

xtb

ook

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te y

our

answ

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ow.

a.H

ow m

any

bloc

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be

in t

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righ

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um

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at t

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pape

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)3

b.

Exp

lain

how

you

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you

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swer

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part

a.

Sam

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answ

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2 b

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om

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Th

ere

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3b

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mai

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rig

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e m

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lock

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th

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nu

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in t

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n i

neq

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ity

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t yo

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3

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on

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6 a

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17 1

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lved

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4

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An

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Skills Practice

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ult

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ER

IOD

____

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7-5

7-5

Sol

ve e

ach

in

equ

alit

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d c

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k y

our

solu

tion

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en g

rap

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Exercises

Example

2Example

2S

olve

} �y 12}

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luti

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212

(4)

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tiply

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mbo

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heck

the

res

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ph t

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solu

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the

Mul

tiplic

atio

n an

d D

ivis

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Pro

pert

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of I

nequ

aliti

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lve

ineq

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n yo

u m

ultip

ly o

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vide

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de o

f an

ineq

ualit

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a p

ositi

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umbe

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e in

equa

lity

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tru

e.T

he d

irect

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x�

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nu

mbe

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an9

into

th

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an

ineq

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rem

ain

true

whe

n m

ultip

lyin

g or

div

idin

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ch s

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of t

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equa

lity

by a

neg

ativ

enu

mbe

r, ho

wev

er,

you

mus

t re

vers

e th

e di

rect

ion

of t

he in

equa

lity

sym

bol.

Example

1Example

1Study Guide and Intervention

So

lvin

g In

equ

alit

ies

by M

ult

iply

ing

or

Div

idin

g

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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ATE

____

____

____

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ER

IOD

____

_

7-5

7-5

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184

32

10

Lesson 7-5



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So

lvin

g In

equ

alit

ies

by M

ult

iply

ing

or

Div

idin

g

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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ATE

____

____

____

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ER

IOD

____

_

7-5

7-5

Ho

w a

re in

equ

alit

ies

use

d in

stu

dyi

ng

sp

ace?

Do

the

acti

vity

at

the

top

of

pag

e 35

0 in

you

r te

xtb

ook

.Wri

te y

our

answ

ers

bel

ow.

a.D

ivid

e ea

ch s

ide

of t

he

ineq

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ity

300 .

50 b

y 2.

Is t

he

ineq

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ity

stil

ltr

ue?

Exp

lain

by

usi

ng

an i

neq

ual

ity.

yes;

150�

25

b.

Wou

ld t

he

wei

ght

of 5

ast

ron

auts

be

grea

ter

on P

luto

or

on E

arth

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xpla

in b

y u

sin

g an

in

equ

alit

y.E

arth

;30

0 �

67,s

o 5

(300

) �

5(67

).

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Act

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Rea

din

g t

he

Less

on

1.D

escr

ibe

the

Mu

ltip

lica

tion

Pro

pert

y of

In

equ

alit

y fo

r bo

th p

osit

ive

and

neg

ativ

e n

um

bers

an

d gi

ve a

n e

xam

ple

of a

pro

blem

for

eac

h t

ype

of n

um

ber.

Wh

en y

ou

m

ult

iply

eac

h s

ide

of

an in

equ

alit

y by

th

e sa

me

po

siti

ve n

um

ber

,th

ein

equ

alit

y re

mai

ns

tru

e.W

hen

yo

u m

ult

iply

eac

h s

ide

of

an in

equ

alit

y by

th

e sa

me

neg

ativ

e n

um

ber

,th

e in

equ

alit

y si

gn

mu

st b

e re

vers

ed f

or

the

ineq

ual

ity

to r

emai

n t

rue.

Stu

den

ts’e

xam

ple

s w

ill v

ary.

2.D

escr

ibe

the

Div

isio

n P

rope

rty

of I

neq

ual

ity

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both

pos

itiv

e an

d n

egat

ive

nu

mbe

rs a

nd

give

an

exa

mpl

e of

a p

robl

em f

or e

ach

typ

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nu

mbe

r.W

hen

yo

u d

ivid

e ea

ch s

ide

of

an in

equ

alit

y by

th

e sa

me

po

siti

ve n

um

ber

,th

e in

equ

alit

y re

mai

ns

tru

e.W

hen

yo

u d

ivid

e ea

ch s

ide

of

an in

equ

alit

y by

th

e sa

me

neg

ativ

e n

um

-b

er,t

he

ineq

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ity

sig

n m

ust

be

reve

rsed

fo

r th

e in

equ

alit

y to

rem

ain

tru

e.S

tud

ents

’exa

mp

les

will

var

y.

Hel

pin

g Y

ou

Rem

emb

er

3.In

th

e bo

xes

belo

w,w

rite

exa

mpl

es o

f in

equ

alit

ies

in w

hic

h t

he

sign

doe

s an

d do

es n

otre

vers

e.W

rite

at

leas

t th

ree

exam

ples

in

eac

h b

ox.

Sam

ple

an

swer

s ar

e g

iven

.

Ineq

uali

ties

in W

hic

hth

e S

ign

Do

es

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t R

evers

e

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5x 4

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y �

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ties

in W

hic

hth

e S

ign

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es

9 � �

3x

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25 �

y

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Practice

So

lvin

g In

equ

alit

ies

by M

ult

iply

ing

or

Div

idin

g

NA

ME

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____

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ATE

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ER

IOD

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7-5

7-5

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Sol

ve e

ach

in

equ

alit

y an

d c

hec

k y

our

solu

tion

.Th

en g

rap

h t

he

solu

tion

on

a

nu

mb

er l

ine.

1.9x

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13.

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CO

UN

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o qu

alif

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r a

stor

e di

scou

nt,

Jorg

e’s

socc

er t

eam

mu

st s

pen

d at

lea

st$5

60 f

or n

ew je

rsey

s.T

he

team

nee

ds 2

0 je

rsey

s.

a.W

rite

an

in

equ

alit

y to

rep

rese

nt

how

mu

ch t

he

team

sh

ould

spe

nd

on e

ach

jers

ey t

oqu

alif

y fo

r th

e di

scou

nt.

20p�

560

b.

How

mu

ch s

hou

ld t

he

team

spe

nd

for

each

jers

ey?

p�

$28

14.

POLI

TIC

SM

i-L

ing

wan

ts t

o m

ail

at l

east

850

fli

ers

enco

ura

gin

g vo

ters

to

vote

for

th

eu

pcom

ing

sch

ool

levy

.Sh

e h

as f

ive

days

to

get

them

all

in

th

e m

ail.

a.W

rite

an

in

equ

alit

y to

rep

rese

nt

how

man

y fl

iers

Mi-

Lin

g m

ust

mai

l ev

ery

day.

5f�

850

b.

How

man

y fl

iers

sh

ould

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Lin

g m

ail

each

day

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43

21

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43

2

Lesson 7-5



An

swer

s

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2G

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re-A

lgeb

ra

Som

e in

equa

litie

s re

quire

mor

e th

an o

ne s

tep

to s

olve

.For

suc

h in

equa

litie

s, u

ndo

the

oper

atio

ns in

reve

rse

orde

r, ju

st a

s in

sol

ving

mul

ti-st

ep e

quat

ions

.

Rem

embe

r to

rev

erse

the

ineq

ualit

y sy

mbo

l whe

n m

ultip

lyin

g or

div

idin

g ea

ch s

ide

of t

he in

equa

lity

by

a ne

gativ

e nu

mbe

r. Sol

ve 1

2 �

2x�

24 �

2xan

d c

hec

k y

our

solu

tion

.Gra

ph

th

e so

luti

onon

a n

um

ber

lin

e.

12 2

2x.

24 1

2xW

rite

the

ineq

ualit

y.

12 2

2x2

2x.

24 1

2x2

2xS

ubtr

act

2xfr

om e

ach

side

.

12 2

4x.

24S

impl

ify.

12 2

12 2

4x.

24 2

12S

ubtr

act

12 f

rom

eac

h si

de.

24x

.12

Sim

plify

.

}2 24 4x }

,} 212

4}D

ivid

e ea

ch s

ide

by –

4 an

d re

vers

e th

e sy

mbo

l.

x,2

3S

impl

ify.

CH

EC

K

122

2x.

241

2xTr

y –4

, a

num

ber

less

tha

n –3

.

12 2

2(2

4) .

24 1

2(2

4)R

epla

ce x

with

–4.

12 1

8 .

24 2

8S

impl

ify.

20 .

16 �

The

sol

utio

n ch

ecks

.

Gra

ph t

he

solu

tion

x,2

3.


So

lvin

g M

ult

i-S

tep

Ineq

ual

itie

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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ATE

____

____

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ER

IOD

____

_

Example

Example

7-6

7-6

Exercises

Exercises

�3

�2

�1

�4

�5

If th

e in

equa

lity

cont

ains

par

enth

eses

, us

e th

e D

istr

ibut

ive

Pro

pert

y to

beg

in s

impl

ifyin

g th

e in

equa

lity.

Sol

ve e

ach

in

equ

alit

y an

d c

hec

k y

our

solu

tion

.Gra

ph

th

e so

luti

on o

n a

nu

mb

er l

ine.

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43

21

07

86

54

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NA

ME

____

____

____

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ATE

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ER

IOD

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7-5

7-5

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lenc

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1G

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re-A

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Hid

den

Wo

rdIn

eac

h g

rou

p o

f fi

ve i

neq

ual

itie

s,on

ly t

wo

hav

e th

e sa

me

solu

tion

set

.For

eac

hgr

oup

,wri

te t

he

solu

tion

of

each

in

equ

alit

y an

d t

hen

cir

cle

the

lett

ers

of t

he

two

ineq

ual

itie

s h

avin

g th

e sa

me

solu

tion

set

.Aft

er c

omp

leti

ng

all

fou

r gr

oup

s,u

se t

he

circ

led

let

ters

to

form

a o

ne-

wor

d a

nsw

er t

o th

e q

ues

tion

at

the

bot

tom

of

the

pag

e.

GR

OU

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scra

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le t

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led

let

ters

to

fin

d t

he

nam

e of

th

e fi

rst

of t

he

orig

inal

13

colo

nie

s to

rat

ify

the

U.S

.Con

stit

uti

on.

Del

awar

e

Lesson 7-5



©G

lenc

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4G

lenc

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Practice

So

lvin

g M

ult

i-S

tep

Ineq

ual

itie

s

NA

ME

____

____

____

____

____

____

____

____

____

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ATE

____

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____

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ER

IOD

____

_

7-6

7-6

Sol

ve e

ach

in

equ

alit

y an

d c

hec

k y

our

solu

tion

.Th

en,g

rap

h t

he

solu

tion

on

an

um

ber

lin

e.

1.2x

112

,2

12x��

122.

6 1

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3.5 2

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c�

13

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12 2

x) .

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c) ,

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c ��

7

9.} 3c }1

7 .

5}1 2}

c��

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p��

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3) .

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x��

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5 2

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c1

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3

13.

2(n

25)#

27

n �

1.5

14.}18

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#6

n �

6

15.

Tw

o ti

mes

a n

um

ber

less

10

is g

reat

er t

han

fiv

e ti

mes

th

e sa

me

nu

mbe

r pl

us

2.F

orw

hat

nu

mbe

r or

nu

mbe

rs i

s th

is t

rue?

x��

4

16.

On

e-h

alf

of t

he

sum

of

a n

um

ber

and

12 i

s le

ss t

han

27.

Wh

at i

s th

e n

um

ber?

n�

42

17.

STA

TE F

AIR

Adm

issi

on t

o th

e st

ate

fair

cos

ts $

5 an

d ea

ch r

ide

cost

s $0

.75.

If A

hm

edw

ants

to

spen

d n

o m

ore

than

$14

at

the

fair

,how

man

y ri

des

can

he

ride

?0.

75r�

5 �

14,r

�12

rid

es

18.

GIF

TSY

uko

wan

ts t

o bu

y te

ddy

bear

s th

at c

ost

$8.5

0 ea

ch f

or h

er e

igh

t n

iece

s an

dn

eph

ews.

Sh

e w

ould

lik

e to

get

a h

at f

or e

ach

ted

dy b

ear,

also

.If Y

uko

wan

ts t

o sp

end

no

mor

e th

an $

94,h

ow m

uch

can

sh

e sp

end

on e

ach

hat

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(8.5

�h

) �

94,h

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.25

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34

56

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23

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54

67

8

Skills Practice

So

lvin

g M

ult

i-S

tep

Ineq

ual

itie

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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ATE

____

____

____

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ER

IOD

____

_

7-6

7-6

©G

lenc

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ill39

3G

lenc

oe P

re-A

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ra

Sol

ve e

ach

in

equ

alit

y an

d c

hec

k y

our

solu

tion

.Gra

ph

th

e so

luti

on o

n a

nu

mb

er l

ine.

1.3x

19 ,

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5 1

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b)b��

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}m 3}1

5 $

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9

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(8 2

x) .

6x ��

48.

} 4c }1

7 $

5c ��

8

9.y2

3 ,

5y1

1y��

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.20

22n

.26

n��

3

11.

}1 3}(x2

6) ,

2x�

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2k #

15k�

10

13.2

2(3 1

t),2

8t �

114

.}n 4}2

9 .

5n

�56

15.

Tw

o ti

mes

a n

um

ber

less

4 i

s gr

eate

r th

an t

he

sam

e n

um

ber

plu

s 6.

For

wh

at n

um

ber

or n

um

bers

is

this

tru

e?n�

10

16.

On

e-h

alf

of t

he

sum

of

a n

um

ber

and

4 is

les

s th

an 1

4.W

hat

is

the

nu

mbe

r?n�

24

17.

FISH

ING

Ben

jam

in w

ants

to

go f

ish

ing

on t

he

lake

.A b

oat

ren

ts f

or $

12 p

er h

our

and

aro

d an

d re

el r

ent

for

$20

per

day.

If h

e w

ants

to

spen

d n

o m

ore

than

$80

,how

man

yh

ours

can

he

spen

d fi

shin

g in

th

e bo

at?

12h�

20 �

80,h

�5

h

18.

ENTE

RTA

ININ

GD

een

a i

s in

viti

ng

10 f

rien

ds t

o a

part

y.If

sh

e w

ants

to

spen

d n

o m

ore

than

$12

0 on

her

gu

ests

,an

d di

nn

er f

or e

ach

gu

est

cost

s $8

,wh

at i

s th

e m

ost

can

sh

esp

end

on p

arty

fav

ors

for

each

per

son

?10

(8 �

f) �

120,

f �

$4

54

32

1�

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5

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23

54

67

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10

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5655

54Lesson 7-6



An

swer

s

©G

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cGra

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ill39

6G

lenc

oe P

re-A

lgeb

ra

Enrichment

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

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ER

IOD

____

_

7-6

7-6

Co

nd

itio

nal

an

d U

nco

nd

itio

nal

Ineq

ual

itie

sW

hen

th

e re

plac

emen

t se

t is

th

e se

t of

rea

l n

um

bers

,th

e in

equ

alit

y 2x

,16

is

call

ed

a co

nd

itio

nal

in

equ

alit

ybe

cau

se i

t is

tru

e fo

r at

lea

st o

ne

but

not

all

val

ues

of

the

repl

acem

ent

set.

Oth

er e

xam

ples

of

con

diti

onal

in

equ

alit

ies

are

x1

5.

8 an

d 2y

26,

10.

If t

he

repl

acem

ent

set

is t

he

set

of r

eal

nu

mbe

rs,x

15.

xis

tru

e fo

r ev

ery

elem

ent

of

the

repl

acem

ent

set.

Su

ch a

n i

neq

ual

ity

is c

alle

d an

un

con

dit

ion

al i

neq

ual

ity.

Oth

er

exam

ples

of

un

con

diti

onal

in

equ

alit

ies

are

2x1

9.

2xan

d x2

7,

x.

Sol

ve e

ach

in

equ

alit

y.T

hen

det

erm

ine

wh

eth

er e

ach

in

equ

alit

y is

con

dit

ion

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r u

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nd

itio

nal

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s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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ATE

____

____

____

__P

ER

IOD

____

_

7-6

7-6

©G

lenc

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cGra

w-H

ill39

5G

lenc

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Ho

w a

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the

top

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pag

e 35

5 in

you

r te

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ook

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answ

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bel

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rite

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in

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at r

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rela

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wee

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b

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Lesson 7-6




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:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. A

B

C

C

A

D

C

D

B

C

180

B

B

B

C

D

C

D

A

B

B

D

A

D

B

C

A

D

C

A

C

D

B

D

B

D

Chapter 7 Assessment Answer Key Form 1 Form 2APage 397 Page 398 Page 399

An

swer

s

(continued on the next page)


11.

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: 16

B

B

B

C

A

D

C

D

B

C

D

B

A

C

C

D

D

C

B

D

C

D

A

B

D

B

C

D

C

B

Chapter 7 Assessment Answer Key Form 2A (continued) Form 2BPage 400 Page 401 Page 402


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.

26.

27.

28.

29.

30.

31.

32.

33.

B:Sample answer:

4x � 5 � 2(2x � 3)

at most 7

6

n � n � 1 � 13;

at least 545 points

�27�28�29 �26 �25 �24

12111098 13 14 1615

�1�2 0 1 2 4 5 63

false

Sample answer:b � 65 � 500

Cecile: 10; Laura: 15; Kami: 5

14, 15, 16

30 ft by 75 ft

Sample answer: 8x � 12x � 4; 1

�

all numbers

56

��45

�

39

�1

2

18

Chapter 7 Assessment Answer Key Form 2CPage 403 Page 404

An

swer

s


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.

26.

27.

28.

29.

30.

31.

32.

33.

B:Sample answer:

3y � 4 � 2(y � 2) � y

at least 16

7

n � n � 1 � 15;at most 7

at least 591 points

b � 8.7

�27�28 �26 �25 �23�24

12111098 13 14 1615

�1�2 0 1 2 4 5 63

false

Sample answer:b � 80 � 600

Bernardo: 18;Kyle: 6; Elan: 12

12, 13, 14

35 ft by 90 ft

9x � 1 � 10x; x � �1

�

all numbers

39

��59

�

9

��23

�

2

�8

Chapter 7 Assessment Answer Key Form 2DPage 405 Page 406

An

swer

s


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:1250(30)x � 25,000(30)

� 30,000; $20.80

513 books

r � ��16

�

no more than $811

at least 13

21,000 � 7,000 or 7,000 � 21,000

Sample Answer: 0.8

�14�15 �13 �12 �10�11

5 rolls

4009 feet

�

�1.5

all numbers

�18

�10

�3.2

Chapter 7 Assessment Answer Key Form 3Page 407 Page 408

all numbers thatare greater than or

equal to �2 andless than 4


Chapter 7 Assessment Answer KeyPage 409, Open-Ended Assessment

Scoring Rubric

Score General Description Specific Criteria

• Shows thorough understanding of the concepts of writingand solving equations and writing, solving, and graphinginequalities.

• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• The graph is accurate, perhaps with additional labels and

explanation.• Goes beyond requirements of some of or all problems.

• Shows an understanding of the concepts of writing andsolving equations and writing, solving, and graphinginequalities.

• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• The graph is accurate.• Satisfies all requirements of problems.

• Shows an understanding of most of the concepts of writingand solving equations and writing, solving, and graphinginequalities.

• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• The graph is 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.• The graph is mostly accurate but lacks detail or

explanation.• Satisfies minimal requirements of some of the problems.

• Shows little or no understanding of the concepts of writingand solving equations and writing, solving, and graphinginequalities.

• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• The graph is inaccurate.• Does not satisfy the 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

Chapter 7 Assessment Answer Key Page 409, Open-Ended Assessment

Sample Answers


1. Sample answer: Admission to anamusement park costs $18. For eachempty soft drink can you bring to thepark, you receive a $2 discount off theregular admission price. The number ofcans you can bring is represented by p.The minimum price of admission is $6.$18.00 � 2p � $6.006 � p

The maximum number of cans you canbring is six.

2. Sample answer: Jason paid for 3 boxes of his favorite cereal with a 10-dollar bill and a 5-dollar bill. Hereceived $2.43 in change. What does onebox of Jason’s favorite cereal cost? Let x � cost of one box of cereal.$10 � $5 � 3x � $2.43 $15 � 3x � $2.43 x � $4.19 One box of Jason’s favorite cereal costs$4.19.

3. The box contains 35 red pens, 15 bluepens, 7 black pens, and 3 green pens.

4a. 3x � 1�34� � 4

4b. x � the weight of one calculator

4c. x � �34�

4d. Each calculator must weigh less

than �34� pound, or 12 ounces.

65432 7 8 109

In addition to the scoring rubric found on page A22, the following sample answers may be used as guidance in evaluating open-ended assessment items.

An

swer

s


Chapter 7 Assessment Answer Key Vocabulary Test/Review Quiz (Lessons 7–1 and 7–2) Quiz (Lessons 7–4 and 7–5)

Page 410 Page 411 Page 412

1. f

2. i

3. d

4. c

5. g

6. e

7. b

8. a

9. j

10. h

11. Sample answer: a mathematicalsentence containinga � or �

12. Sample answer: an equation true forevery value of thevariable

1.2.3.

4.

5.

6.

7.

8.

9.

10.

Quiz (Lesson 7–3)

Page 411

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

Quiz (Lesson 7–6)

Page 412

1.

2.

3.

4.

5.

�1�2�3�4 0 1 2 43

65432 7 8 109

65432 7 8 109

�7�6�5�4�3�2�1�8�9

�7�6�5�4�3�2�1�8�9

C

�1�2 0 1 2 4 5 63

�1�2�3�4�5�6 0 1 2

�1�2�3�4 0 1 2 43

true

true

w: 17 in.; �: 5 in.;A: 85 in2

Sample answer:3x � 5x � 36; 18

�0.7all numbers

�

11063

�6


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

x � 3�25

�

n � �7�35

�

At least 11 pairs

8

�170�

$110.49

43�34

�%

�418�

�1�56

�

48a2b

1�373�

2, 5, 10

�48ab

�1�2 0 1 2 4 5 63

�

2

2

C

C

A

D

B

Chapter 7 Assessment Answer Key Mid-Chapter Test Cumulative ReviewPage 413 Page 414

An

swer

s


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17. 18.

19.

20. x � 48

$630; $441; $309; $216

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

1 3 3

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

2 2 5

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

Chapter 7 Assessment Answer KeyStandardized Test Practice

Page 415 Page 416

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