37 R.3 Real Number Operations and Properties 95. a- 2 9 - 1 4b - c - 5 18 - a- 1 2b d 96. c - 5 8 - a- 2 5b d - a 3 2 - 11 10b 97. -8 + 1-421-62 , 12 4 - 1-32 98. 15 , 5 # 4 , 6 - 8 -6 - 1-52 - 8 , 2 Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. 99. -p2 - 7q + r2 100. -p2 - 2q + r 101. q + r q + p 102. p + r p + q 103. 3q r - 5 p 104. 3r q - 2 r 105. 5r 2p - 3r 106. 3q 3p - 2r 107. q 2 - r 3 3p 4 + q 8 108. q 4 - r 5 p 2 + q 2 109. -1p + 222 - 3r 2 - q 110. -1q - 622 - 2p 4 - p 111. 3p + 314 + p23 r + 8 112. 5q + 211 + p23 r + 3 Concept Check Identify the property illustrated in each statement. Assume all variables represent real numbers. 113. 6 # 12 + 6 # 15 = 6112 + 152 114. 81m+ 42 = 8m+ 32 115. 1t - 62 # a 1 t - 6b = 1, if t - 6≠0 116. 2 + m 2 - m # 2 - m 2 + m =1, if m≠2 or -2 117. 17.5 - y2 + 0 = 7.5 - y 118. 1 # 13x - 72 = 3x - 7 119. 51t + 32 = 1t + 32 # 5 120. -7 + 1x + 32 = 1x + 32 + 1-72 121. 15x2a 1 xb = 5ax # 1 xb 122. 138 + 992 + 1 = 38 + 199 + 12 123. 5 + 23 is a real number. 124. 5p is a real number. Write a short answer to each question. 125. Is there a commutative property for subtraction? That is, in general, is a - b equal to b - a? Support your answer with an example. 126. Is there an associative property for subtraction? That is, does 1a - b2 - c equal a - 1b - c2 in general? Support your answer with an example. Simplify each expression. See Examples 7 and 8. 127. 10 11 122z2 128. a 3 4 rb1-122 129. 1m+ 52 + 6 130. 8 + 1a + 72 131. 3 8 a 16 9 y + 32 27 z - 40 9 b 132. - 1 4 120m+8y -32z2 Rewrite each expression using the distributive property and simplify, if possible. See Example 8. 133. 8p - 14p 134. 15x - 10x 135. -41z - y2 136. -31m+ n2
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