Section 2.5 Compound Inequalities 113 SECTION 2.5 EXERCISE SET Write About It! Use complete sentences in your answer to each exercise. 1. Explain the meaning of the intersection of sets. 2. Explain the meaning of the union of sets. 3. Is it possible for the intersection of two sets to be the empty set? Explain. 4. Is it possible for the union of two sets to be the empty set? Explain. 5. What is a compound inequality? 6. Explain the difference of the graphs of compound inequalities -a < x < a and x < -a or x > a, where a > 0. 7. How do you find the solutions of a compound inequality involving “and”? 8. How do you find the solutions of a compound inequality involving “or”? Practice Makes Perfect! Find the intersection and union of the following sets. Write each solution set in interval notation. (See Objectives 1 and 2.) 9. A = (-10, 6), B = -4, 2 10. A = (-8, 3), B = -7, 1 11. A = -10, -3, B = -9, -3 12. A = -13, -5, B = -12, -5 13. A = 6, 20, B = (6, 20) 14. A = -7, 5, B = (-7, 5) 15. A = (-∞, 7) , B = -1, 7 16. A = (-∞, -2, B = -4, -2) 17. A = (-11, ∞), B = (-∞, 11) 18. A = (-∞, 53), B = (-53, ∞) 19. A = -12, 5, B = (-10, 8) 20. A = -2, 10, B = (-4, 6) Solve each compound inequality. Write each solution set in interval notation. (See Objective 3.) 21. x ≤ 5 and x≥-1 22. x ≤ 1 and x≥-10 23. x > 3 and x < 2 24. x ≤ 8 and x > 10 25. 2x + 4 > 8 and 3x < 9 26. 9x + 3 > 12 and 10x ≤ 40 27. 3x + 6 ≥ 3 and 7x - 13<-20 28. 6x - 1 > 17 and 4x - 5 ≤ 29 29. 6 - 4x > 2 and 1 - 3x < 5 30. 7 - 8x> -1 and 2 - 5x < 2 31. 9x + 11 ≥ 2 and 4x - 3≤-7 32. 12x + 1 ≥ 13 and 5x - 6≤-1 33. 5(3x - 2) ≤ 15 and 2(4x + 1) ≥ 10 34. 4(2x - 3) ≤ 6 and 3(5x + 10) ≥ 0 35. x > 7 and x > 5 36. x≤-3 and x≤-7 37. 6x - 5 > 1 and 7x + 6 > 20 38. 4x - 3 > 5 and 5x - 1 ≥ 9 39. 3x - 2 ≥ 10 and 1 - 3x < 40 40. 2x - 7 > 0 and 1 - 2x < 15 41. 6 - 3x > 4 and 2 - 2x > 10 42. 3 - 10x ≤ 23 and 10 - 11x ≤ 43 43. 3x + 9 ≥ 4 and 9x>-15 44. 4x - 1 ≤ 11 and 3x < 9 45. 2(4x - 3) < 4 and 6(x - 5) < 12 46. 4(2x + 1) > 5 and 8(x - 2) > 3 Solve each compound inequality. Write each solution set in interval notation. (See Objective 4.) 47. x<-3 or x > 1 48. x<-4 or x > 0 49. x≥-7 or x < 3 50. x > 2 or x ≤ 10 51. x ≤ 0 or x ≤ 6 52. x ≥ 10 or x ≥ 15 53. 11x - 3 ≥ 52 or 6x ≤ 42 54. 13x<-52 or 3 - 5x > 17
hendricks_intermediate_algebra_1e_ch1_3
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