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Additional info for 501 Algebra Questions, 2nd edition
14 + 9(2w + 7) + −2(6 + −w) Use the distributive property of multiplication on the second term. [9(2w + 7) = 9 · 2w + 9 · 7] [9 · 2w + 9 · 7 = 18w + 63] Use the distributive property of multiplication on the third term. [−2(6 + −w) = −2 · 6 + −2 · −w] Notice the result of multiplication for opposite and like-signed terms. [−2 · 6 + −2 · −w = −12 + +2w] Substitute the results into the original expression. 14 + (18w + 63) + (−12 + +2w) Parentheses are no longer needed. 14 + 18w + 63 + −12 + +2w Use the commutative property of addition to put like terms together.
Use the associative property for addition. Add like terms. Signs different? Subtract the value of the terms. Substitute the result into the expression. The simpliﬁed algebraic expression is: 6a + 8b + 7a + (−7b) 6a + 7a + 8b + (−7b) (6a + 7a) + (8b + −7b) [6a + 7a = 13a] [8b + −7b = b] (13a) + (b) 13a + b 58. Use the distributive property of multiplication on the ﬁrst term. Use the distributive property of multiplication on the second term. Substitute the result into the expression. Use the commutative property for addition to put like terms together.
3x − 9 = 15 104. 5x − 6 = −26 x 105. ᎏ3ᎏ + 4 = 10 x 106. ᎏ7ᎏ − 5 = 1 107. 36 = 3a − 9 108. 4 = 4a + 20 109. 10a + 5 = 7 110. 25 = 1 2 111. ᎏ3ᎏm + 8 = 20 3 112. 9 = ᎏ4ᎏm − 3 113. 41 − 2m = 61 114. 4m − 14 = 50 2m 115. ᎏ5ᎏ + 16 = 24 116. 5 117. 10s − 6 = 0 s 118. 7 = 3 119. 8s − 5 = 35 120.