Question

Which expressions are equivalent to 2 (three-fourths x 7) minus 3 (one-half x minus 5)? Check all that apply. -1 29 2 (three-fourths x 7) (negative 3) left-bracket one-half x (negative 5) right-bracket 2 (three-fourths x) 2 (7) 3 (one-half x) 3 (negative 5) 2 (three-fourths x) 2 (7) (negative 3) (one-half x) (negative 3) (negative 5).

Answer 1

The expression is equivalent to $\rm 2(\dfrac{3}{4}x ) + 2(7) + (-3) ( \dfrac{1}{2}x) + (-3) (-5)$.

Given that

Expression; $2 \left ( \dfrac{3}{4}x+7 \right ) -3 \left ( \dfrac{1}{2}x - 5 \right )$

We have to determine

Which expressions are equivalent to the given expression.

According to the question

Expression; $2 \left ( \dfrac{3}{4}x+7 \right ) -3 \left ( \dfrac{1}{2}x - 5 \right )$

To solve the given expression follow all the steps given below.

By applying the distributive property of multiplication;

$\rm a(b+c) = ab +ac$

Then,

The equivalent expression is,

$= 2 \left ( \dfrac{3}{4}x+7 \right ) -3 \left ( \dfrac{1}{2}x - 5 \right )\\ \\ = ( 2 \times \dfrac{3}{4}x) + ( 2\times 7 ) -(3 \times \dfrac{1}{2}x)-( 3 \times - 5 )\\ \\ = 2(\dfrac{3}{4}x ) + 2(7) + (-3) ( \dfrac{1}{2}x) + (-3) (-5)$

Hence, the expression is equivalent to $\rm 2(\dfrac{3}{4}x ) + 2(7) + (-3) ( \dfrac{1}{2}x) + (-3) (-5)$.

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