Preview Warm Up California Standards Lesson Presentation

Warm Up Solve. 1. 2x + 8 = x – 7 2. –4(x + 3) = –5x – 2 3. 5x + x + (–11) = 25 – 3x 4. 6n + 9 – 4n = 3n x = –15 x = 10 x = 4 n = 9

AF4.0 Students solve simple linear equations and inequalities over the rational numbers. Also covered: AF1.1 California Standards

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.

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. Remember!

Solve and graph. a 4 12 < a 4 4 • 12 < 4 • Multiply both sides by 4. 48 < a, or a > 48 43 44 45 46 47 48 49 50 51 52 53 54

Check According to the graph, 49 should be a solution and 47 should not be a solution. 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.

Solve and graph. –9b ≤ 45 ≥ 45 –9 – 9b –9 Divide both sides by –9; ≤ changes to ≥ BECAUSE WE DIVIDED BY A NEGATIVE. b ≥ –5 –5

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 73 74 75 76 77 78 79 80 81 82 83 84

Check According to the graph, 79 should be a solution and 81 should not be a solution. 16 > b 5 16 > b 5 Substitute 79 for b. Substitute 81 for b. 16 > 79 5 ? 16 > 81 5 ? 16 > 15.8 ? 16 > 16.2 ? x So 79 is a solution. So 81 is not a solution.

Solve and graph. 12 ≤ –4a ≥ –4a –4 12 –4 Divide both sides by –4; ≤ changes to ≥ BECAUSE WE DIVIDED BY A NEGATIVE. –3 ≥ a –3

–2 1. –14x > 28 2 x < –2 x 3 2. < 15 50 40 45 x < 45 Lesson Quiz: Part I Solve and graph. 1. –14x > 28 –2 2 x < –2 x 3 2. < 15 50 40 45 x < 45 3. 18 < –6x -8 -6 -4 -2 –3 > x q 8 4.  5 q ≥ 40 40 45

Lesson Quiz: Part II 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