Example

Solve for $w$: $\quad -5|w-7|+2 = -13$

Solution

In order to use our procedure for solving absolute value equations, we must first get the value value expression on one side by itself. To do so, we subtract $2$ and then divide by $-5$:

Now this absolute value equation is equivalent to the compound equation

We solve each equation separately, starting with the equation on the left.

or

The first equation has solution $w=10$.

Now we solve the equation on the right.

or

The second equation has solution $w=4$.

The solution of the original absolute value equation is the union of the two solutions: