#### Answer

$x=24\text{ or }x=-24$

#### Work Step by Step

We start with the given equation: $|x|-9=15$
First, we must isolate the absolute value term by adding $9$ on both sides: $$|x|+9-9=15+9$$$$|x|=24$$ We must determine all values $x$ that are $24$ units away from $0$ on a number line. We find that both $24$ and $-24$ satisfy this condition.
Therefore, $x=24\text{ or }x=-24$