Question

which expressions are equivalent to $4\left(\frac{3}{4}y - 2 + \frac{1}{2}y\
ight)$? choose all that apply. $-3y$ $3y + 8 + 2y$ $5y - 8$ $5y + 8$ $4y - 8$ $3y - 8 + 2y$

Explanation:

Step1: Simplify terms inside parentheses

Combine like $y$-terms:
$\frac{3}{4}y + \frac{1}{2}y - 2 = \frac{3}{4}y + \frac{2}{4}y - 2 = \frac{5}{4}y - 2$

Step2: Distribute the 4 to all terms

Multiply each term by 4:
$4 \times \frac{5}{4}y - 4 \times 2$

Step3: Calculate the simplified expression

Simplify the products:
$5y - 8$

Step4: Check other equivalent forms

Combine like terms in $3y - 8 + 2y$:
$3y + 2y - 8 = 5y - 8$

Answer:

$5y - 8$, $3y - 8 + 2y$