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Additional resources for 501 Algebra Questions, 2nd edition
The simpliﬁed algebraic expression is: 29 Team-LRN [2(x + y) = 2 · x + 2 · y] [2x + 2y] (4x + 8y) + (2x + 2y) (4x + 2x + 8y + 2y (4x + 2x) + (8y + 2y) [4x + 2x = 6x] [8y + 2y = 10y] (6x) + (10y) 6x + 10y 501 Algebra Questions 57. Use the distributive property of multiplication on the ﬁrst term. [2(3a + 4b) = 2 · 3a + 2 · 4b] [6a + 8b] Use the distributive property of multiplication on the second term. [7(a − b) = 7 · a − 7 · b] [7a − 7b] (6a + 8b) + (7a − 7b) 6a + 8b + 7a − 7b Substitute the results into the expression.
Perform the numerical operation in the parentheses. Zero is the identity element for addition. 77. Add 25 to each side of the equation. Use the commutative property for addition. Associate like terms. Perform the numerical operation in the parentheses. Zero is the identity element for addition. 78. Subtract 17 from both sides of the equation. Associate like terms. Change subtraction to addition and change the sign of the term that follows. Apply the rules for operating with signed numbers. Zero is the identity element for addition.
Divide both sides of the equation by 2. Apply the rules for operating with signed numbers. 2a ÷ 2 = 18 ÷ 2 a = 18 ÷ 2 aᎏᎏ= ᎏᎏ9 ᎏ 2a ᎏᎏ 2 18 = ᎏ2ᎏ a=9 Another method is as follows: 87. Divide both sides of the equation by 4. Apply the rules for operating with signed numbers. Another look for this solution method is as follows: 88. Divide both sides of the equation by −3. Apply the rules for operating with signed numbers. 89. Divide both sides of the equation by 27. 4x ÷ 4 = −20 ÷ 4 x = −20 ÷ 4 − xᎏᎏ= ᎏᎏᎏ5 ᎏ 4x ᎏᎏ 4 20 = −ᎏ4ᎏ x = −5 −3y ᎏ− ᎏ 3 18 = ᎏ−3ᎏ 18 y = ᎏ−3ᎏ y = −6 27b ᎏᎏ 27 9 = ᎏ27ᎏ 9 b = ᎏ27ᎏ Reduce fractions to their simplest form.
501 Algebra Questions, 2nd edition by LearningExpress