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Linear Equations Warm-Up Lesson: Solve and Graph

Practice solving linear equations and inequalities using rational numbers. Learn to reverse inequality symbols when multiplying/dividing by negative numbers. Understand graphing inequalities on a number line. Includes example problems and solutions.

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Linear Equations Warm-Up Lesson: Solve and Graph

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 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

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

  4. 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.

  5. 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.

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

  7. 12 < 12 < 12 < 12 < 12 < 12.25 12 < 11.75 a 4 a 4 49 4 47 4 ? ? ? ? Check According to the graph, 49 should be a solution and 47 should not be a solution. Substitute 49 for a. Substitute 47 for a. x So 49 is a solution. So 47 is not a solution.

  8. 45–9 –9b–9 ≥ Solve and graph. –9b ≤ 45 Divide both sides by –9; ≤ changes to ≥ BECAUSE WE DIVIDED BY A NEGATIVE. b ≥ –5 0 –5

  9. b 5 5• 16 > 5 • Solve and graph. b 5 16 > Multiply both sides by 5. 80 > b, or b < 80 73 74 75 76 77 78 79 80 81 82 83 84

  10. 16 > 16 > 16 > 16 > 16 > 15.8 16 > 16.2 b 5 b 5 79 5 81 5 ? ? ? ? Check According to the graph, 79 should be a solution and 81 should not be a solution. Substitute 79 for b. Substitute 81 for b. x So 79 is a solution. So 81 is not a solution.

  11. –4a–4 12–4 ≥ Solve and graph. 12 ≤ –4a Divide both sides by –4; ≤ changes to ≥ BECAUSE WE DIVIDED BY A NEGATIVE. –3 ≥ a 0 –3

  12. –2 0 2 40 50 45 x q 3 8 -8 -6 -4 -2 45 40 Lesson Quiz: Part I Solve and graph. 1. –14x > 28 x< –2 2. < 15 x< 45 3. 18< –6x –3 > x 4. 5 q ≥ 40

  13. 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

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