Precalculus (6th Edition) Blitzer

The solution set is $\left\{ -2,5 \right\}$
\begin{align} & \left| x \right|=\pm x \\ & 2x-3=7 \\ & 2x=10 \\ & x=5 \end{align} Now, \begin{align} & 2x-3=-7 \\ & 2x=-4 \\ & x=-2 \end{align} Thus, the solution is $\left\{ -2,5 \right\}$