Question

How do you solve `abs(y - 5)- 2 = 10`?

Answer 1

If we want a `y` to make `abs(y - 5)- 2 = 10`, we'll need a `y` that makes `abs(y - 5) = 12`. (Add 2 to both sides.)

There are two numbers whose absolute value is 12, namely 12 and - 12.

So we need either: `y-5 = 12` and `y=17`

or `y-5=-12` so `y = - 7`

Check both answers (to make sure neither is extraneous).
Both are OK, so they are the solutions.