3 7 Solving Inequalities by Multiplying and Dividing

3 -7 Solving Inequalities by Multiplying and Dividing Preview Evaluating Algebraic Expressions Warm Up California Standards Lesson Presentation

3 -7 Solving Inequalities by Multiplying and Dividing Warm Up Solve. Evaluating Algebraic Expressions 1. 2 x + 8 = x – 7 x = – 15 2. – 4(x + 3) = – 5 x – 2 x = 10 3. 5 x + (– 11) = 25 – 3 x x = 4 4. 6 n + 9 – 4 n = 3 n n=9

3 -7 Solving Inequalities by Multiplying and Dividing Evaluating Algebraic Expressions California Standards AF 4. 0 Students solve simple linear equations and inequalities over the rational numbers. Also covered: AF 1. 1

3 -7 Solving Inequalities by Multiplying and Dividing Evaluating Algebraic Expressions When you MULTIPLY OR DIVIDE both sides of an inequality by a negative number, you must REVERSE the inequality symbol to make the statement true.

3 -7 Solving Inequalities by Multiplying and Dividing Evaluating Algebraic Expressions Remember! When graphing an inequality on a number line, an open circle means that the point is not part of the solution and a closed circle means that the point is part of the solution.

3 -7 Solving Inequalities by Multiplying and Dividing Evaluating Algebraic Expressions 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

3 -7 Solving Inequalities by Multiplying and Dividing Check Evaluating Algebraic Expressions According to the graph, 49 should be a solution and 47 should not be a solution. 12 < a 4 ? 49 12 < 4 Substitute 49 for a. ? 12 < a 4 ? 47 12 < 4 Substitute 47 for a. ? 12 < 12. 25 12 < 11. 75 x So 49 is a solution. So 47 is not a solution.

3 -7 Solving Inequalities by Multiplying and Dividing Evaluating Algebraic Expressions Solve and graph. – 9 b ≤ 45 – 9 b ≥ 45 – Divide both sides by – 9; ≤ changes to ≥ 9 – 9 BECAUSE WE DIVIDED BY A NEGATIVE. b ≥ – 5 0

3 -7 Solving Inequalities by Multiplying and Dividing Evaluating Algebraic Expressions 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

3 -7 Solving Inequalities by Multiplying and Dividing Check Evaluating Algebraic Expressions According to the graph, 79 should be a solution and 81 should not be a solution. 16 > b 5 ? 79 16 > 5 Substitute 79 for b. ? 16 > b 5 ? 81 16 > 5 ? Substitute 81 for b. x 16 > 15. 8 16 > 16. 2 So 79 is a solution. So 81 is not a solution.

3 -7 Solving Inequalities by Multiplying and Dividing Evaluating Algebraic Expressions Solve and graph. 12 ≤ – 4 a 12 ≥ – 4 a – 4 – 3 ≥ a Divide both sides by – 4; ≤ changes to ≥ BECAUSE WE DIVIDED BY A NEGATIVE. – 3 0

3 -7 Solving Inequalities by Multiplying and Dividing Lesson Quiz: Part I Solve and graph. Evaluating Algebraic Expressions 1. – 14 x > 28 x < – 2 x 2. < 15 3 x < 45 – 2 0 2 40 50 45 3. 18 < – 6 x – 3 > x q 5 q ≥ 40 4. 8 -8 -6 -4 -2 40 45

3 -7 Solving Inequalities by Multiplying and Dividing Lesson Quiz: Part II Evaluating Algebraic Expressions 5. Jared isn’t supposed to carry more than 35 pounds in his backpack. He has 8 textbooks and each book weighs 5 pounds. What is the greatest amount of textbooks he can carry in his backpack at one time? No more than 7