solve each inequality. 1. x – 15 > 3 2. g + 3 ≤ –20 3. 11 ≥ t – 8 solve each...

Solve each inequality.

1. x – 15 > 3

2. g + 3 ≤ –20

3. 11 ≥ t – 8

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

4. 34 < 6 + d

5. 5 – f ≥ 10

6. Jonas has $75 to spend on new clothes. The pair of jeans he

wants costs $48.50. What is the most Jonas can spend on shirts?

Course 2, Lesson 6-7

ANSWERS

1. x > 18

2. g ≤ –23

3. t ≤ 19

4. d > 28;

5. f ≤ –5;

6. $26.50


WHAT does it mean to say two quantities are equal?

Expressions and Equations


• 7.EE.4Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

• 7.EE.4bSolve word problems leading to inequalities of the form px + q > ror px + q < r, where p, q, and r are specific rational numbers. Graphthe solution set of the inequality and interpret it in the context ofthe problem.

Course 2, Lesson 6-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.


Mathematical Practices

1 Make sense of problems and persevere in solving them.

2 Reason abstractly and quantitatively.

3 Construct viable arguments and critique the reasoning of others.

4 Model with mathematics.

7 Look for and make use of structure.

Course 2, Lesson 6-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.


• To solve inequalities when multiplying or dividing by a positive number

• To solve inequalities when multiplying

or dividing by a negative number





•Multiplication Property of Inequality•Division Property of Inequality

Multiplication and Division Properties of Inequality,Positive Number



Words The and the state that an inequality

remains true when you multiply or divide each side of an inequality by a positive number.

Symbols For all numbers a, b, and c, where c > 0,

1. if a > b, then ac > bc and

2. if a < b, then ac < bc and

These properties are also true for a ≥ b and a ≤ b.

Multiplication Property of InequalityDivision Property of Inequality

.a bc c

.a bc c

Multiplication and Division Properties of Inequality, Negative Number



Words When you multiply or divide each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true.

Symbols For all numbers a, b, and c, where c < 0,

1. if a > b, then ac < bc and

2. if a < b, then ac > bc and

Examples 7 > 1 –4 < 16

–2(7) < –2(1) Reverse the symbols >

–14 < –2 1 > –4 These properties are also true for a ≥ b and a ≤ b.

.a bc c

.a bc c

44

16

4

How did what you learned today help you answer the


Course 2 Lesson 6-7


How did what you learned today help you answer the


Course 2 Lesson 6-7


Sample answers:• To keep the same inequality sign when multiplying or

dividing each side of an inequality by a positive number

• To reverse the inequality sign when multiplying or dividing each side of an inequality by a negative number

How did the previous lessonon solving inequalities byadding or subtracting helpyou with today’s lesson?

Ratios and Proportional Relationships


Course 2 Lesson 6-7

solve each inequality. 1. x – 15 > 3 2. g + 3 ≤ –20 3. 11 ≥ t – 8 solve each...

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