Question

Use the expression below to answer the question. 20 + 8y – 9y – 21 Which expression is equivalent? A. 2(10 + 4y – 7y – 19) B. 2(10 + 4y) – 3(3y – 7) C. 4(5 + 2y – 5y – 17) D. 4(5 + 2y) – 3(3y + 7)

Answer 1

Option D: $4(5+2y)-3(3y+7)$ is the correct answer.

Explanation:

The expression is $20+8 y-9 y-21$

Solving the expression, we have,

$-y-1$

Now, we need to find an expression equivalent to $20+8 y-9 y-21$

Option A: $2(10+4y-7y-19)$

Solving the expression, we have,

$\begin{aligned} 2(10+4 y-7 y-19) &=2(-9-3 y) \\ &=-18 y-6 y \end{aligned}$

From the result, the expression $2(10+4y-7y-19)$ is not equivalent to $20+8 y-9 y-21$

Option A is not the correct answer.

Option B: $2(10+4 y)-3(3 y-7)$

Solving the expression, we have,

$\begin{aligned} 2(10+4 y)-3(3 y-7) &=20+8 y-9 y+21 \\ &=-y+41 \end{aligned}$

From the result, the expression $2(10+4 y)-3(3 y-7)$ is not equivalent to $20+8 y-9 y-21$

Option B is not the correct answer.

Option C: $4(5+2y-5y-17)$

Solving the expression, we have,

$\begin{aligned} 4(5+2 y-5 y-17) &=20+8 y-20 y-68 \\ &=-12 y-48 \end{aligned}$

From the result, the expression $4(5+2y-5y-17)$ is not equivalent to $20+8 y-9 y-21$

Option C is not the correct answer.

Option D: $4(5+2 y)-3(3 y+7)$

Solving the expression, we have,

$\begin{aligned} 4(5+2 y)-3(3 y+7) &=20+8 y-9 y-21 \\ &=-y-1 \end{aligned}$

From the result, the expression $4(5+2 y)-3(3 y+7)$ is equivalent to $20+8 y-9 y-21$

Option D is not the correct answer.