Answer
$$x=-\frac{3}{2}\quad \mathrm{or}\quad \:x=5$$
Work Step by Step
Solving the equation using the rules of Algebra, we find:
$$\left|4x-7\right|=13 \\ 4x-7=-13\quad \mathrm{or}\quad \:4x-7=13 \\ x=-\frac{3}{2}\quad \mathrm{or}\quad \:x=5$$