#### Answer

$x=20\text{ or }x=-20$

#### Work Step by Step

We start with the given equation: $|x|+7=27$
First, we must isolate the absolute value term by subtracting $7$ from both sides: $$|x|+7-7=27-7$$$$|x|=20$$ We must determine all values $x$ that are $20$ units away from $0$ on a number line. We find that both $20$ and $-20$ satisfy this condition.
Therefore, $x=20\text{ or }x=-20$