Answer
$$x=-1\quad \mathrm{or}\quad \:x=\frac{9}{2}$$
Work Step by Step
Since the value inside the absolute value can be positive or negative and get the same number, we must consider both options. Doing this, we find:
$$ 4x-7=-11\quad \mathrm{or}\quad \:4x-7=11\\ x=-1\quad \mathrm{or}\quad \:x=\frac{9}{2}$$
