Answer
The correct solution is $-15\lt x \lt 25$.
Work Step by Step
The given inequality is
$\Rightarrow |x-5|\lt 20$
Write a compound inequality.
$\Rightarrow x-5\lt 20$ and $x-5\gt -20$
Add $5$ to each side.
$\Rightarrow x-5+5\lt 20+5$ and $x-5+5\gt -20+5$
Simplify.
$\Rightarrow x\lt 25$ and $x\gt -15$
Hence, the correct solution is $-15\lt x \lt 25$.
