Solving Multi-Step Inequalities ALGEBRA 1 LESSON 3-4 21. n 9 22. w < 3 23. t –1 24. d 6 25. n 2 26. k –4 27. s < 10 28. p > 3 29. x > 2 30. m > – 31. d < –1 32. y –1 pages 155–159  Exercises 1. d 4 2. m > –3 3. x > –2 4. n 3 5. q 4 6. h –2 7. a 3 8. b > 6 9. c < 2 < – 11. 27 2s + 8 and s 9.5, so the two equal sides must be no longer than 9.5 cm. 12. –6x + 9 13. j 1 14. b < 15. h > 5 16. x 3 17. y > –8 18. w 4 19. c < –7 20. r 2 > – < – < – < – 1 2 < – < – > – > – > – 1 3 > – > – < – > – 1 c 1 2 1 4 10. 8t 420 and t 52.5, so the average rate of speed must be at least 52.5 mi/h. < – > – > – 1 2 < – < – 3-4

Solving Multi-Step Inequalities ALGEBRA 1 LESSON 3-4 33. k 34. v –4 35. q –2 36. r 1 37. x < 1 38. m > –8 39. v 2 40. Subtract 8 from each side. 41. Subtract 7 from each side. 42. Subtract y from each side and add 5 to each side. 43. Add 2 to each side, then multiply each side by –5, and reverse the inequality sign. 44. Subtract 3j from each side and subtract 5 from each side. 45. Answers may vary. Sample: Multiply q – 3 by 2, add 3q to each side, add 6 to each side, and divide each side by 5. 46. a. –3t –9, t 3 b. 9 3t, t 3 c. The results are the same. 47. 6 – (r + 3) < 15, r > –12 48. (t – 6) 4, t 14 2 3 > – > – < – 4 5 > – 1 3 > – < – > – < – > – 1 2 < – < – 3-4

Solving Multi-Step Inequalities ALGEBRA 1 LESSON 3-4 49. 3(z + 2) > 12, z > 2 50. Answers may vary. Sample: To solve 2.5(p – 4) > 3(p + 2), first use the Distributive Property to simplify each side. The result is 2.5p – 10 > 3p + 6. Then use the Subtraction Property of Inequality. Subtract 6 from each side and 2.5p from each side. The result is –16 > 0.5p. Then use the Division Divide each side by 0.5. The result is –32 > p. So the solution is –32 > p or p < –32. 51. a. i. always true ii. always true iii. never true b. If the coefficients of the only variable on each side of an inequality are the same, then the inequality will either be always true or never true. 52. For x = the number of guests, (0.75)200 + 1.25x 250; x 80; at least 80 guests must attend. 53. a. maximum b. no more than 135 54. B 55. E 56. F > – > – 3-4

Solving Multi-Step Inequalities ALGEBRA 1 LESSON 3-4 57. A 58. D 59. C 60. Answers may vary. Samples: – x – 5 > 0, x < –15; – x – 5 10, x –45 61. r < 5 62. m –2 63. s 4.4 64. n –2 65. s < 8 66. k 1.4 77. For x = number of hours of work each month, 15x – (490 + 45 + 65) 600, so to make a profit he must work at least 80 h per month. 78. For x = amount of sales, 250 + 0.03x 460, so to reach her goal, she must have at least $7000 in sales. 79. Add 2x to each side rather than subtract 2x, so x . 80. Distribute 4 to 2 as well as n, so n > –7. 81. a. x > b. x < 67. n > –2 68. r 1 69. x > 1 70. a 71. m 1 72. k 2 73. n –23 74. x 0 75. a < –6 76. c 4 3 4 < – > – 1 2 > – 1 3 > – > – 1 3 < – > – 1 6 < – 1 2 > – > – < – 2 5 < – < – 2 3 5 8 < – > – c – b a < – c – b a 3-4

Solving Multi-Step Inequalities ALGEBRA 1 LESSON 3-4 82. x is an integer between –3 and 7, inclusive. 83. 8.8 in.  14.2 in. 84. –2 85. 10 h 86. a. 74 boxes b. 5 trips 87. C 88. F 89. A 90. F 91. [2] Maxwell should continue ordering from the current 92. m –4 93. y –8 94. x > –12 95. t –3 96. b < 27 97. w > –98 98. p > 1 99. d 7 100. 6 h 101. –16 102. 16 103. 24 104. –16 supplier. Let x = number of bottles Maxwell orders per month. The cost from the current supplier is 3x + 25. The cost from the competitor is 4x + 5. The inequality 4x + 5 3x + 25 represents the number of bottles of shampoo for which the competitor will be less expensive. Since x = 20, the competitor will not be less expensive for orders of 30 bottles or more. (OR equivalent explanation) [1] incorrect answer OR insufficient explanation < – > – > – < – 1 3 > – 3-4