Example

Solve for $x$: $\quad |2x-7|=0$

Solution

This equation has the absolute value expression on the left all by itself and a zero on the right. Because the number on the right is not a positive number, we can treat this equation as a kind of special case.

The only way that $|2x-7|$ can be zero is if $2x-7=0$. The absolute value equation is equivalent to the equation

or

The solution of the original absolute value equation is the single number $x=7/2$.