Section 4: Solutions

# Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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• davidvictor
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Section 1.4 Compound Inequalities 63 Version: Fall 2007 1.4 Exercises In Exercises 1 - 12 , solve the inequality. Express your answer in both interval and set notations, and shade the solution on a number line. 1. 8 x 3 ≤ − 16 x 1 2. 6 x 6 > 3 x + 3 3. 12 x + 5 ≤ − 3 x 4 4. 7 x + 3 ≤ − 2 x 8 5. 11 x 9 < 3 x + 1 6. 4 x 8 ≥ − 4 x 5 7. 4 x 5 > 5 x 7 8. 14 x + 4 > 6 x + 8 9. 2 x 1 > 7 x + 2 10. 3 x 2 > 4 x 9 11. 3 x + 3 < 11 x 3 12. 6 x + 3 < 8 x + 8 In Exercises 13 - 50 , solve the compound inequality. Express your answer in both interval and set notations, and shade the solution on a number line. 13. 2 x 1 < 4 or 7 x + 1 ≥ − 4 14. 8 x + 9 < 3 and 7 x + 1 > 3 15. 6 x 4 < 4 and 3 x +7 ≥ − 5 16. 3 x + 3 8 and 3 x 6 > 6 Copyrighted material. See: 1 17. 8 x + 5 ≤ − 1 and 4 x 2 > 1 18. x 1 < 7 and 6 x 9 8 19. 3 x + 8 ≤ − 5 or 2 x 4 ≥ − 3 20. 6 x 7 < 3 and 8 x 3 21. 9 x 9 9 and 5 x > 1 22. 7 x + 3 < 3 or 8 x 2 23. 3 x 5 < 4 and x + 9 > 3 24. 8 x 6 < 5 or 4 x 1 3 25. 9 x + 3 ≤ − 5 or 2 x 4 9 26. 7 x + 6 < 4 or 7 x 5 > 7 27. 4 x 2 2 or 3 x 9 3 28. 5 x + 5 < 4 or 5 x 5 ≥ − 5 29. 5 x + 1 < 6 and 3 x + 9 > 4 30. 7 x + 2 < 5 or 6 x 9 ≥ − 7 31. 7 x 7 < 2 and 3 x 3 32. 4 x + 1 < 0 or 8 x + 6 > 9 33. 7 x + 8 < 3 and 8 x + 3 ≥ − 9 34. 3 x < 2 and 7 x 8 3 35. 5 x + 2 ≤ − 2 and 6 x + 2 3 36. 4 x 1 8 or 3 x 9 > 0 37. 2 x 5 1 and 4 x + 7 > 7 38. 3 x + 1 < 0 or 5 x + 5 > 8

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64 Chapter 1 Preliminaries Version: Fall 2007 39. 8 x + 7 9 or 5 x + 6 > 2 40. x 6 ≤ − 5 and 6 x 2 > 3 41. 4 x 8 < 4 or 4 x + 2 > 3 42. 9 x 5 < 2 or 8 x 5 ≥ − 6 43. 9 x 5 ≤ − 3 or x + 1 > 3 44. 5 x 3 6 and 2 x 1 6 45. 1 ≤ − 7 x 3 2 46. 0 < 5 x 5 < 9 47. 5 < 9 x 3 6 48. 6 < 7 x + 3 2 49. 2 < 7 x + 6 < 6 50. 9 < 2 x + 5 1 In Exercises 51 - 62 , solve the given in- equality for x . Graph the solution set on a number line, then use interval and set- builder notation to describe the solution set. 51. 1 3 < x 2 + 1 4 < 1 3 52. 1 5 < x 2 1 4 < 1 5 53. 1 2 < 1 3 x 2 < 1 2 54. 2 3 1 2 x 5 2 3 55. 1 < x x + 1 5 < 2 56. 2 < x 2 x 1 3 < 4 57. 2 < x + 1 2 x + 1 3 2 58. 3 < x 1 3 2 x 1 5 2 59. x < 4 x < 5 60. x < 2 x + 3 7 61. x < x + 5 11 62. 2 x < 3 x 8 63. Aeron has arranged for a demon- stration of “How to make a Comet” by Professor O’Commel. The wise profes- sor has asked Aeron to make sure the auditorium stays between 15 and 20 de- grees Celsius (C). Aeron knows the ther-
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