Question

Which expressions are equivalent to 2(3/4x+7)- 3{1/2x-5)? Check all that apply.

-1
29
2(3/4x+7)-3[1/2x+(-5)]
2(3/4x)+2(7)+3(1/2x)+3(-5)
2(3/4x)+2(7)+(-3)(1/2x)+(-3)(-5)

Answer 1

(a) 2(3/4x+7)-3[1/2x+(-5)]

(c) 2(3/4x)+2(7)+(-3)(1/2x)+(-3)(-5)

Explanation:

Adding -5 is equivalent to subtracting 5, so ...

(1/2x -5) = (1/2x +(-5)) . . . . transformation shown in 1st rewrite

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When the number outside parentheses is negative, that negative value multiplies each term inside parentheses:

-3(1/2x +(-5)) = (-3)(1/2x) +(-3)(-5) . . . . shown in 3rd rewrite

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The expressions equivalent to the original are ...

(a) 2(3/4x+7)-3[1/2x+(-5)]

(c) 2(3/4x)+2(7)+(-3)(1/2x)+(-3)(-5)