Answer
$x\leq-1\text{ or }x\geq8$
See graph
Work Step by Step
Apply absolute rule:
If $|u|\geq a,~a\gt 0$, then $u\leq-a\text{ or }u\geq a$.
Take $u=7-2x$ and $a=9$.
$$7-2x\leq-9\text{ or }7-2x\geq9$$
$$7-2x-7\leq-9-7\text{ or }7-2x-7\geq9-7$$
$$-2x\leq-16\text{ or }-2x\geq2$$
$$\frac{-2x}{-2}\geq\frac{-16}{-2}\text{ or }\frac{-2x}{-2}\leq\frac{2}{-2}$$
$$x\geq8\text{ or }x\leq-1$$
Rearranging:
$$x\leq-1\text{ or }x\geq8$$
The graph of the solution set is as shown.
