Solve the equation.

Question

–4y + 8 = 4(2y – 2) – 2(–16 + 8y)
(1 point)
Responses

y = –4
y = –4

y = 4
y = 4

y = –2
y = –2

y = –6
y = –6

Answer 1

To solve the equation –4y + 8 = 4(2y – 2) – 2(–16 + 8y), we start by simplifying both sides.

–4y + 8 = 4(2y – 2) – 2(–16 + 8y)

First, we distribute on the right side:
–4y + 8 = 8y – 8 – 2(-16 + 8y)

Next, we simplify the expression inside the parentheses:
–4y + 8 = 8y – 8 + 32 - 16y

Combining like terms:
–4y + 8 = -8y + 24

Now, we can isolate the variable y by subtracting -8y from both sides and adding 8 to both sides:
–4y + 8 - (-8y) = -8y + 24 - (-8y) + 8
–4y + 8 + 8y = 24

Combining like terms:
4y + 8 = 24

Next, we subtract 8 from both sides:
4y + 8 - 8 = 24 - 8
4y = 16

Finally, we divide both sides by 4 to solve for y:
4y/4 = 16/4
y = 4

Therefore, the solution to the equation –4y + 8 = 4(2y – 2) – 2(–16 + 8y) is y = 4.