Transcript 11-4
11-4 Solving Inequalities by Multiplying and Dividing 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 11-4 Solving Inequalities by Multiplying and Dividing Learn to solve and graph inequalities by using multiplication or division. 11-4 Solving Inequalities by Multiplying and Dividing 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! 11-4 Solving Inequalities by Multiplying and Dividing Example 1: Solving Inequalities by Multiplying or Dividing Solve and graph. 12 < a 4 4 • 12 < 4 • a 4 Multiply both sides by 4. 48 < a, or a > 48 43 44 45 46 47 48 49 50 51 52 53 54 11-4 Solving Inequalities by Multiplying and Dividing 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 < 49 4 Substitute 49 for a. 12 < a 4 ? 12 < 47 4 Substitute 47 for a. 12 < 12.25 12 < 11.75 x So 49 is a solution. So 47 is not a solution. ? ? 11-4 Solving Inequalities by Multiplying and Dividing Example 2: Solving Inequalities by Multiplying or Dividing Solve and graph. –9b ≤ 45 -9b ≥ 45 Divide both sides by -9; ≤ changes to ≥. -9 -9 b ≥ -5 –5 0 11-4 Solving Inequalities by Multiplying and Dividing Example 3 Solve and graph. 16 > b 5 5 • 16 > 5 • b 5 Multiply both sides by 5. 80 > b, or b < 80 73 74 75 76 77 78 79 80 81 82 83 84 11-4 Solving Inequalities by Multiplying and Dividing Example 4 Solve and graph. -4a > 12 -4a ≥ 12 Divide both sides by -4; ≤ changes to ≥. –4 –4 a < -3 –3 0 11-4 Solving Inequalities by Multiplying and Dividing Example 5 Solve and graph. 3x ≤ -18 11-4 Solving Inequalities by Multiplying and Dividing Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 11-4 Solving Inequalities by Multiplying and Dividing Lesson Quiz: Part I Solve and graph. 1. –14x > 28 x < –2 x 2. < 15 3 x < 45 3. 18 < –6x –3 > x q 5 4. 8 q ≥ 40 11-4 Solving Inequalities by Multiplying and Dividing 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 11-4 Solving Inequalities by Multiplying and Dividing 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