98 Chapter 2 Linear Equations and Inequalities in One Variable 15. -9 < x≤-4 16. 0 < x ≤ 2 17. -4 ≤ x ≤ 0 18. 5 ≤ x ≤ 6 19. 3 < x 20. 4 ≤ x 21. -2 > x≥-10 22. 3 ≥ x>-6 23. -10 ≥ x 24. -9 ≥ x 25. x > 0 26. x > 14 27. x ≥ 1 3 28. x≥- 1 4 29. x<-5 30. x<-16 31. -15 < x<-4 32. -1 ≤ x < 45 33. -13 > x 34. -26 > x 35. 11 < x 36. 5 ≤ x 37. 1 ≥ x ≥ 0 38. -7 ≥ x>-20 Solve each inequality. Graph the solution set and write the answer in interval notation and set-builder notation. (See Objective 2.) 39. y + 9>-3 40. y - 10 > 6 41. 6a ≤ 12 42. 3a ≤ 24 43. 2x - 10 < 0 44. 5x - 15 > 0 45. 6x + 11≥-7 46. 7x - 1 ≥ 8 47. -3x < 14 48. -4x ≤ 15 49. b + 14 ≥ 6b - 9 50. 2b - 8 < 4b + 1 51. 16≤-12a 52. -24≤-6a 53. 4a + 15 < 13a - 9 54. a - 16 ≤ 6a + 10 55. 5(x - 1) > 4(2x + 1) 56. 6(3x + 2) ≥ 3(7x - 1) 57. 2 3 (x + 3)<-x + 5 58. 5 2 (x - 4)≥-2x + 8 59. 1 4 (5x - 2) ≥ 1 3 (2x + 9) 60. 1 2 (3x + 8) ≤ 2 3 (4x - 1) Write an inequality that represents each situation. Solve the inequality and explain the answer using a complete sentence. (See Objective 3.) 61. If Lucinda’s quiz scores are 85, 78, 100, and 87, what must she earn on her fifth quiz to have an average of at least 90? 62. If Aaron’s quiz scores are 66, 79, 60, and 65, what must he earn on his fifth quiz to have an average of at least 70? 63. Aleksandr’s course grade is based on a weighted average. The weights are as follows: homework (15%), quizzes (25%), tests (40%), and final exam (20%). If Aleksandr’s homework average is 80, quiz average is 60, and test average is 68, what must he score on the final exam to have an average of at least 70? 64. Christopher’s course grade is based on a weighted average. The weights are as follows: homework (15%), quizzes (25%), tests (40%), and final exam (20%). If Christopher’s homework average is 100, quiz average is 75, test average is 80, what must he score on the final exam for his course average to be at least 80? 65. Connect2Me charges a monthly fee of $39.99 for 450 anytime cell phone minutes, and then $0.45 per additional minute. If Joyce budgets $60 each month for her cell phone, how many additional minutes can she afford to use? 66. MobileMania charges a monthly fee of $29.99 for 200 anytime cell phone minutes, and then $0.30 per additional minute. If Sandra budgets $45 each month for her cell phone, how many additional minutes can she afford to use? 67. Rebecca pays $1500 for a reception hall for her son’s graduation party, and she is charged $15 per person for a buffet by the caterer. If Rebecca budgets $3000 for the reception hall and the caterer, how many people can Rebecca invite to her son’s party? 68. Ilene is planning her office Christmas party. She finds a banquet hall at a local hotel that charges $700, and the hotel will also prepare dinner for $30 per person. If Ilene has a budget of $2000, how many people can attend the Christmas party? The total U.S. national health expenditures, in trillions of dollars, can be approximated by the equation E = 0.118x + 2.03, where x is the number of years after 2005. (Source: http://www.cms.gov) 69. In what year will the total national health expenditures exceed $3 trillion? 70. In what year will the total national health expenditures exceed $3.2 trillion? The total national health expenditures for the Department of Veterans’ Affairs, in billions of dollars, can be approximated by the equation, V = 3.154x + 28.94, where x is the number of years after 2005. (Source: http:// www.cms.gov) 71. In what year will the total national health expenditures for the Department of Veterans’ Affairs exceed $51 billion?
hendricks_intermediate_algebra_1e_ch1_3
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