Question

How do you solve `8- ( 4y - 7) = 1- 5y`?

Answer 1

See a solution process below:

Explanation:

First, remove the terms from the parenthesis on the left side of the equation being careful to handle the signs correctly and then group and combine like terms:

`8 - 4y + 7 = 1 - 5y`

`8 + 7 - 4y = 1 - 5y`

`15 - 4y = 1 - 5y`

Now, subtract `color(red)(15)` and add `color(blue)(5y)` to each side of the equation to solve for `y` while keeping the equation balanced:

`15 - color(red)(15) - 4y + color(blue)(5y) = 1 - color(red)(15) - 5y + color(blue)(5y)`

`0 + (-4 + color(blue)(5))y = -14 - 0`

`1y = -14`

`y = -14`

Answer 2

`y=-14`

Explanation:

We essentially have a `-1` out in front of the parenthesis. Let's distribute that to the inner terms to get

`8-4y+7=1-5y`

We can combine like terms on the left to get

`-4y+15=1-5y`

We can add `5y` to both sides to get

`y+15=1`

Remember, we only want a `y` on the left. Next, we can subtract `15` from both sides to get

`y=-14`

Hope this helps!