Answer
$x\leq-14.5\text{ or }x\geq-5.5$
See graph
Work Step by Step
$$2|x+10|\geq9$$
$$\frac{2|x+10|}{2}\geq\frac{9}{2}$$
$$|x+10|\geq\frac{9}{2}$$
Apply absolute rule:
If $|u|\geq a,~a\gt 0$, then $u\leq-a\text{ or }u\geq a$.
Take $u=x+10$ and $a=\frac{9}{2}$.
$$x+10\leq-\frac{9}{2}\text{ or }x+10\geq\frac{9}{2}$$
$$x+10-10\leq-\frac{9}{2}-10\text{ or }x+10-10\geq\frac{9}{2}-10$$
$$x\leq\frac{-9-20}{2}\text{ or }x\geq\frac{9-20}{2}$$
$$x\leq-\frac{29}{2}\text{ or }x\geq-\frac{11}{2}$$
$$x\leq-14.5\text{ or }x\geq-5.5$$
The graph of the solution set is as shown.
