Answer
$-12\lt x \lt -2$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 5|x+7|\lt 25$
Divide each side by $5$.
$\Rightarrow \frac{5|x+7|}{5}\lt \frac{25}{5}$
Simplify.
$\Rightarrow |x+7|\lt 5$
Write a compound inequality.
$\Rightarrow x+7\lt 5$ and $x+7\gt -5$
Subtract $7$ from each side.
$\Rightarrow x+7-7\lt 5-7$ and $x+7-7\gt -5-7$
Simplify.
$\Rightarrow x\lt -2$ and $x\gt -12$
Hence, the solution is $-12\lt x \lt -2$.
