Question

\In order to solve for the variable in the equation 1 minus (x + 2) + 2 x = 5 (2 x minus 5) minus x, Mikel first applies the distributive property. Which equation is a result of this step?

1 minus x + 2 + 2 x = 10 x minus 5 minus x
1 minus x minus 2 + 2 x = 10 x minus 25 minus x
1 minus x minus 1 + 2 x = 10 x minus 25 minus x
1 minus x minus 1 + 2 x = 10 x minus 5 minus x

Answer 1

(b) 1 - x - 2 + 2 x = 10 x - 25 - x

Explanation:

The distributive property tells you the factor outside parentheses multiplies each term inside parentheses.

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application

1 -(x +2) +2x = 5(2x -5) -x

The minus sign outside the parentheses on the left side of the equal sign represents a factor of -1. Using the distributive property there, we have ...

1 +(-1)(x) +(-1)(2) +2x = 5(2x -5) -x

1 -x -2 +2x = 5(2x -5) -x . . . . . . simplify a bit

The 5 outside parentheses on the right side of the equal sign similarly multiplies each of the terms inside those parentheses:

1 -x -2 +2x = (5)(2x) +(5)(-5) -x

1 -x -2 +2x = 10x -25 -x . . . . . . . . matches the second choice

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Additional comment

It might be helpful to think of parentheses as a "bag." The factor outside tells you how many bags you have. (All are the same.) When you eliminate the parentheses, you are essentially dumping the contents of the bags into one pile. Since all of the bags have the same contents, the total is the product of what's in a bag and the number of bags.