76 Chapter 1 Real Numbers and Algebraic Expressions 9. Distributive property 10. How to apply distributive property to simplify an expression Practice Makes Perfect! Find the additive inverse and the multiplicative inverse of each number. Assume all variables are nonzero. (See Objective 1.) 11. -7 12. 8 13. 25 14. -12 15. 3 5 16. 7 4 17. - 4 9 18. - 3 10 19. 3x 20. 12y 21. -6a 22. -5b 23. x 6 24. 2y 5 25. - 7a 2 26. - 4b 3 Apply the commutative and associative properties to rewrite each expression and simplify the result. (See Objective 2.) 27. 4 + x + 7 28. 9 + y + 5 29. -12 + a - 1 30. -15 + b - 7 31. -6 + x + (-10) 32. -18 + y + (-12) 33. 3(x)(9) 34. 5( y)(15) 35. (-1)(a)(-16) 36. (-1)(b)(-24) 37. 5(x)(-14) 38. -9( y)(4) 39. (c - 6) + (-3) 40. (d - 12) + (-9) 41. x - (-2) - 12 42. y - (-28) - (-15) 43. -2(3x) 44. -8(2y) 45. -7(-3a) 46. -4(-5b) 47. a- 1 2 b + x + 3 4 48. 2 3 + y - 5 12 49. aa + 5 7 b + 2 50. ab - 3 5 b + 2 51. 12(x)a1 6 b 52. 18(y) a5 6 b 4 xb 54. - 5a 7 10 yb 53. -6a1 Apply the distributive property to rewrite each expression. Simplify the result. (See Objective 3.) 55. 4(x - 7) 56. 5(x - 9) 57. 3(x + 5) 58. 6(x + 2) 59. 11(3x - 4) 60. 12(5x - 3) 61. 6(2x + 3y - 5) 62. 3(5x - 2y + 10) 63. -(-5x + 2y -9) 64. -11(3x + 4y - 6) 65. -(16x - 3) 66. -(23x - 12) 67. 12a- 1 2 x + 1 3 b 68. 10a- 1 5 x + 1 2 b 69. -12a3 2 x - 1 4 b 70. -24a1 6 x - 3 8 b Mix ’Em Up! Find the additive inverse and the multiplicative inverse of each number. Assume all variables are nonzero. 71. 15x 72. -2a 73. 6x 7 74. 3c 5 75. -11 76. 21 77. 9 5 78. - 6 5 Apply the commutative, associative, and/or distributive properties to rewrite each expression and simplify the result. 79. 8 + x + 12 80. -12 + b - 4 81. 2(x)(14) 82. 3( y)(19) 83. -8 + x + (-28) 84. -4 + y + (-22) 85. (-1)(a)(-18) 86. -7(y)(14) 87. x - (-5) - 19 88. y - (-17) - (-1) 89. a- 3 5 b + a + 1 2 90. - 1 3 + b - 5 6 91. 4(2.1a) 92. 3(1.2b) 93. aa - 7 8 b + 1 94. ab - 7 10 b + 1 95. -(-x - 12y + 5) 96. 8(2x - 3y + 1) 97. -2(7x) 98. -9(-5b) 99. 5(-0.3x + 0.2) 100. 2(-0.9x + 0.1) 101. -5(2x + 3) 102. -(12x + 5) 103. 12(x)a- 1 4 b 104. -5a- 3 10 yb 105. 6 a- 1 6 x + 1 3 b 106. 0.4(1.5x - 0.3) 107. 0.8(0.7x - 1.2) 108. 5a- 1 10 x + 2 5 b You Be the Teacher! Correct each student’s errors, if any. 109. Simplify 3(2a). Josh’s work: 3(2a) = 3(2)(3a) = 6(3a) = 18a 110. Simplify 3(6x + 2y - 4). Grace’s work: 3(6x + 2y - 4) = 18x + 2y - 4 111. Simplify -(2 - x + 3y). Charlotte’s work: -(2 - x + 3y) = -2 - x + 3y 112. Simplify -6(-4b). Mary’s work: -6(-4b) = -6(-4)(-6b) = 24(-6b) = -144b
hendricks_beginning_algebra_1e_ch1_3
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