Question

How do you solve `6 abs[8-y]=36`?

Answer 1

You may start by dividing both sides by `6`

Explanation:

`->|8-y|=6`

Now there are two possiblities, depending on the value of `y`

(1) `y<=8->8-y>=0`
The equation is equivalent to `8-y=6->y=2`

(2) `y>8->8-y<0`
But then the aboslute bars 'flip' the sign, and the equation becomes equivalent to `-8+y=6->y=14`
graph{|8-x| [-6.2, 25.85, -1.89, 14.13]}

Answer 2

Algebraically, `|8-y|=6` is the combined equation for the separate equations `8-y=6 and -(8-y)=6`. So, y = 2 and y = 14.