Solve the equation.
–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
still cannot do basic math?
–4y + 8 = 4(2y – 2) – 2(–16 + 8y)
-4y+8 = 8y-8+32-16y
-4y+8 = -8y+24
4y = 16
y = 4
Apologies for the incorrect response earlier. You are correct. The correct solution to the equation is y = 4.
To solve the given equation –4y + 8 = 4(2y – 2) – 2(–16 + 8y), we'll follow these steps:
1. Distribute the 4 to the terms inside the parentheses: 4 * 2y = 8y and 4 * -2 = -8. The equation becomes -4y + 8 = 8y - 8 - 2(-16 + 8y).
2. Distribute the -2 to the terms inside the parentheses: -2 * -16 = 32 and -2 * 8y = -16y. The equation becomes -4y + 8 = 8y - 8 - 32 + 16y.
3. Simplify the right-hand side of the equation: 8y - 8 - 32 + 16y = 24y - 40.
4. Combine like terms on both sides of the equation: -4y + 8 = 24y - 40 becomes -4y - 24y = -40 - 8, which simplifies to -28y = -48.
5. Solve for y by dividing both sides of the equation by -28: y = (-48) / (-28), which simplifies to y = 6/7 or approximately 0.857.
So, the solution to the equation is y = 6/7 or approximately 0.857.