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hendricks_intermediate_algebra_1e_ch1_3

Section 1.3 Properties of Real Numbers and Simplifying Algebraic Expressions 43 Translate each phrase or sentence into an algebraic expression, equation, or inequality. Use the variable x to represent the unknown number. (See Objective 4.) 69. Three less than a number 70. Twelve less than a number 71. Six more than twice a number 72. Seven more than three times a number 73. A number divided by 6 74. The ratio of a number and 4 75. Half the difference between a number and 11 76. One-third the sum of a number and 5 77. Thirteen is ten more than twice a number. 78. Two is three less than four times a number. 79. Five more than twice a number is greater than the number plus 3. 80. Six less than four times a number is less than two more than twice the number. 81. The total of eight and a number yields half the sum of the number and 5. 82. The total of nine and twice a number results in one-half the difference between the number and 10. Solve each problem. (See Objective 5.) 83. Marty invests $6000 in two different stocks. If x represents the amount invested in one stock, write an expression for the amount invested in the other stock. 84. Emma spends $534 on two evening dresses. If she spends x dollars on the fi rst dress, how much did she spend on the second dress? 85. Ricky has been collecting pennies and nickels in a jar and he has 20 fewer nickels than pennies. a. If x represents the number of pennies Ricky has collected, write an expression for the number of nickels he has collected. b. Write an expression for the value, in cents, of the nickels Ricky has collected. c. Write an expression for the value, in cents, of the pennies Ricky has collected. d. If Ricky’s collection is worth $1.70, write an equation that represents this total value, in cents. 86. Diana has been saving $2 bills and silver dollars. She has 10 fewer $2 bills than silver dollars. a. If x represents the number of silver dollars Diana has saved, write an expression for the number of $2 bills she has saved. b. Write an expression for the value, in dollars, of Diana’s silver dollars. c. Write an expression for the value, in dollars, of Diana’s $2 bills. d. If Diana has $40 total, write an equation that represents the total value of her collection. 87. The American Association of Colleges of Nursing found that enrollment in entry-level baccalaureate nursing programs increased by 5.7% from 2009 to 2010. If x represents the enrollment in baccalaureate nursing programs in 2009, write an expression for the enrollment in 2010. (Source: http://www.aacn.nche.edu/ media/factsheets/nursingshortage.htm) 88. The number of adults in the United States who own an e-book reader in May 2011 increased by 100% over the number who owned one in November 2010. If x represents the number who owned an e-book reader in November 2010, write an expression for the number who owned one in May 2011. (Source: http://pewresearch .org/pubs/?Year=2011) Mix ’Em Up! Find the additive inverse and multiplicative inverse for each expression. Assume all denominators are nonzero. 89. x -5 90. x + 2 91. 4 a 92. b 3 93. 3 x + 1 94. x + 3 2 Identify the property that is used to rewrite each expression. 95. (5x - 29) + 70y = 5x + (-29 + 70y) 96. (3x - 10) + 6y = 3x + (-10 + 6y) 97. 6(v - u) · 9 = 6(v - u) · 9 98. 7(g + h) · 4 = 7(g + h) · 4 99. (x + y)(m + n) = (x + y)m + (x + y)n 100. (x + y)(m + n) = (m + n)(x + y) Simplify each expression. 101. a3 - 5a2 + 12a + 6a2 - 8a + 17 102. 2b3 - 7b2 - 15b + 10 - 3b2 + 9b - 21 103. 1 3 (6x - 3) + 3 4 8(x - 1) + 10 104. 3 4 (4x - 12) - 5 2 4(3 - x) - 3 105. 0.035m + 0.042(3000 - m) 106. 0.064x + 0.032(4500 - x) 107. 4(m - 3) + 2(m2 - 5) 108. 12(2b + 4) - 4(b2 + 3) 109. 3 5 x - 2 5 - 1 5 x + 7 5 110. 3 4 x - 7 5 - 5 4 x + 1 5


hendricks_intermediate_algebra_1e_ch1_3
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