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Published byDarrell Townsend Modified over 6 years ago

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Problem of the Day Find an integer x that makes the following three inequalities true: 9 < x < 14, 2x > 22, and –x > –13 x = 12

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**Learn to solve and graph inequalities by using multiplication or division.**

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**If you multiply or divide BY a negative, switch your sign!**

The steps for solving inequalities by multiplying or dividing are the same as for solving equations, with one exception. If both sides of an inequality are multiplied or divided by a negative number, the inequality symbol must be reversed. Copy in Notes: If you multiply or divide BY a negative, switch your sign!

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**Example 1: Solving Inequalities by Multiplying or Dividing**

Solve and graph. a 4 12 < 4 • 12 < 4 • a 4 Multiply both sides by 4. 48 < a, or a > 48

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**Additional Example 1A Continued**

Check According to the graph, 49 should be a solution because 49 > 48, and 47 should not be a solution because 47 < 48. 12 < a 4 12 < a 4 Substitute 49 for a. Substitute 47 for a. 12 < 49 4 ? 12 < 47 4 ? 12 < 12.25 ? 12 < 11.75 ? x So 49 is a solution. So 47 is not a solution.

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**Example 2: Solving Inequalities by Multiplying or Dividing**

Solve and graph. –9b ≤ 45 ≥ 45 -9 -9b -9 Divide both sides by -9; ≤ changes to ≥. b ≥ -5 –5

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**Example 3 Solve and graph. b 5 16 > b 5 Multiply both sides by 5.**

5 • 16 > 5 • b 5 Multiply both sides by 5. 80 > b, or b < 80

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Example 4 Solve and graph. -4a > 12 ≥ 12 –4 -4a –4 Divide both sides by -4; ≤ changes to ≥. a < -3 –3

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Example 5 Solve and graph. 3x ≤ -18

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Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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**1. –14x > 28 x < –2 x 3 2. < 15 x < 45 3. 18 < –6x**

Lesson Quiz: Part I Solve and graph. 1. –14x > 28 x < –2 x 3 < 15 x < 45 3. 18 < –6x –3 > x q 8 4. 5 q ≥ 40

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**Lesson Quiz for Student Response Systems**

1. Choose the inequality that represents the graph. A. p < 7 B. p > 7 C. p > 7 D. p < 7

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**Lesson Quiz for Student Response Systems**

2. Choose the inequality that represents the graph. A. 3p < –9 B. 3p > 9 C. 3p > –9 D. –3p > 9

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