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Name the property: If a > b , then a + c > b + c .

Exercise. Name the property: If a > b , then a + c > b + c. Addition Property of Inequality. Exercise. If a > b and c > 0, then ac ___ bc. >. Exercise. If a > b and c < 0, then ac ___ bc. <. Exercise. Solve x + 3 < 5. x < 2. Exercise.

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Name the property: If a > b , then a + c > b + c .

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  1. Exercise Name the property: If a > b, then a + c > b + c. Addition Property of Inequality

  2. Exercise If a > b and c > 0, then ac ___ bc. >

  3. Exercise If a > b and c < 0, then ac ___ bc. <

  4. Exercise Solve x + 3 < 5. x < 2

  5. Exercise Solve –2x > 8. x < –4

  6. Properties of Inequalities If a < b, then a + c < b + c. Property 6 < 7 and 6 + 3 < 7 + 3; i.e., 9 < 10 Example

  7. Properties of Inequalities If a < b, then a – c < b – c. Property – 4 < – 2 and – 4 – 5 < – 2 – 5; i.e., – 9 < – 7 Example

  8. Properties of Inequalities If a < b and c > 0, then ac < bc. Property 2 < 5 and 2(3) < 5(3); i.e., 6 < 15 Example

  9. Properties of Inequalities If a < b and c < 0, then ac > bc. Property 2 < 5 and 2(– 3) < 5(– 3); i.e., – 6 > – 15 Example

  10. If a < b and c > 0, then < . ac bc 82 42 4 < 8 and < ;i.e., 2 < 4 Properties of Inequalities Property Example

  11. If a < b and c < 0, then > . ac bc 4– 2 8– 2 4 < 8 and ;i.e., – 2 > – 4 > Properties of Inequalities Property Example

  12. multiplying by a negative x4 – > 10 x < – 40 • dividing by a negative – 3x < 6 x > – 2 Reverse signs if:

  13. –4 –4 Example 1 Solve –4x + 3 > 23, and graph the solution. –4x + 3 – 3 > 23 – 3 –4x > 20 x < – 5 – 6 – 5 – 4 – 3 – 2 – 1 0

  14. 34 – x + 8 – 8 ≤ 23 – 8 5 43 34 43 – – – x ≤ 15 Example 2 34 Solve – x + 8 ≤ 23, and graph the solution. x ≥ –20

  15. Example 2 34 Solve – x + 8 ≤ 23, and graph the solution. x ≥ –20 – 30 – 20 – 10 0 10

  16. –2 –2 Example 3 Solve –2(r + 4) > 19, and graph the solution. –2r – 8 > 19 –2r – 8 + 8 > 19 + 8 –2r > 27 r < –13.5

  17. Example 3 Solve –2(r + 4) > 19, and graph the solution. r < –13.5 – 16 – 15 – 14 – 13 – 12

  18. 4 4 Example 4 Solve 2x ≥ – 2x + 8. 2x+ 2x ≥ – 2x+ 2x + 8 4x ≥ 8 x ≥ 2

  19. 2 2 Example 5 Solve 3x – 1 < x + 9. 3x – 1 – x < x + 9 – x 2x – 1 < 9 2x – 1 + 1 < 9 + 1 2x < 10 x < 5

  20. –4 –4 Example 6 Solve 5x – 8 ≤ 9x + 2. 5x – 8 – 9x ≤ 9x + 2 – 9x –4x – 8 ≤ 2 –4x – 8 + 8 ≤ 2 + 8 –4x ≤ 10 x ≥ –2.5

  21. Example Solve 5x + 3 < –7. x < –2

  22. Example Solve –3x + 5 > 17. x < –4

  23. Example Solve 2x – 12 < 7x + 13. x > –5

  24. 25 n > – Example Solve 2(n + 7) > –3n + 12.

  25. Example Solve 3(y – 12) < – 2(y – 9) + 1. y < 11

  26. Example Solve 2.5(x – 3) – 3(x – 2.5) > 2x. x < 0

  27. Example Solve 8(0.75x – 0.375) < 12(1.25x + 0.5). x > –1

  28. Example b5 Solve + 3 ≥ 12. b ≥ 45

  29. Example b + 35 Solve ≥ 12. b ≥ 57

  30. Example a – 95 a + 37 Solve ≤ . a ≥ 39

  31. Exercise Using the inequality ax – b ≤ c, and assuming that a, b, and c are real numbers with a ≠ 0, solve the inequality for x. Be careful to account for all possible values of a, b, and c.

  32. Exercise xr Using the inequality + s > t, and assuming that r, s, and t are real numbers, solve the inequality for x. Be careful to account for all possible values of r, s, and t.

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