Explanation:
18. The 5 only needs to be "distributed" to terms that are inside the parentheses where 5 is on the outside. Here, the only term in the parentheses is 2x. Anne apparently also multiplied -3 by 5, erroneously. The -3 term is not inside the parentheses, so should be left alone when "distributing" the 5.
The left side of the equation simplifies to 10x -3, so Anne should have had ...
10x -3 = 20x +15
-18 = 10x . . . . . . . . . add -15-10x
-1.8 = x . . . . . . . . . . divide by 10.
The solution is x = -1.8.
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19. Procedure: Subtract the right side of the equation from both sides. Use the distributive property as many times as necessary to eliminate parentheses. Collect terms. Divide by the coefficient of x. Subtract the constant.
5[3(x+4) -2(1 -x)] -x -15 = 14x +45 . . . . . . . original equation
5[3(x+4) -2(1 -x)] -x -15 -14x -45 = 0 . . . . . right side subtracted
5[3x+12 -2 +2x] -x -15 -14x -45 = 0 . . . . . . inner parentheses eliminated
15x +60 -10 +10x -x -15 -14x -45 = 0 . . . . . outer parentheses eliminated
(15 +10 -1 -14)x +(60 -10 -15 -45) = 0 . . . . . like terms associated
10x -10 = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . simplified
x - 1 = 0 . . . . . . . . . divide by the coefficient of x
x = 1 . . . . . . . . . . . . subtract -1 (same as add 1)
The solution is x = 1.
