Lesson 6-2

Solving Inequalities by Multiplication and Division

Definition

• Multiplication Property of Inequalities- If each side of a true inequality is multiplied by the same positive number, the resulting inequality is true.

• If each side of a true inequality is multiplied by the same negative number, the direction of the inequality symbol must be reversed so that the resulting inequality is also true.

Solve . Then check your solution.

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b

7≥ 25

Ex 1 Multiply by a positive number

Solve . Then check your solution.

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g

3<12

Multiply by a positive number

Solve . Then check your solution.

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−2

5p < −14

Multiply by a negative numberEx 2

Solve . Then check your solution.

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−3

4d ≥ 6

Multiply by a negative number

Write and solve an inequality

Write an inequality for the sentence below. Then solve the inequality.One fourth of a number is less than -7.

One fourth of a number is less than -7.

n -7

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1

4

Write and solve an inequality

Write an inequality for the sentence below. Then solve the inequality.Four-fifths of a number is at most twenty.

Definition

• Division Property of Inequalities- If each side of a true inequality is divided by the same positive number, the resulting inequality is true.

• If each side of a true inequality is divided by the same negative number, the direction of the inequality symbol must be reversed so that the resulting inequality is also true.

Solve 14h > 91. Then check your solution.

Ex 4 Divide by a positive number

Solve 12s 60. Then check your solution.

Divide by a positive number

Solve -5t 275. Then check your solution.

Divide by a negative numberEx 5

Solve -8q < 138. Then check your solution.

Divide by a negative number