Example

Solve for $x$: $\quad |2x+4|=8$

Solution

This absolute value equation is equivalent to the compound equation

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

or

or

The first equation has solution $x=2$.

Now we solve the equation on the right.

or

or

The second equation has solution $x=-6$.

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