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

Apr 3, 2015

If we want a $y$ to make $\left\mid y - 5 \right\mid - 2 = 10$, we'll need a $y$ that makes $\left\mid y - 5 \right\mid = 12$. (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.