Answer
$b\lt -12$ or $b\gt -4$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 5|b+8|-7\gt 13$
Add $7$ to each side.
$\Rightarrow 5|b+8|-7+7\gt 13+7$
Simplify.
$\Rightarrow 5|b+8|\gt 20$
Divide each side by $5$.
$\Rightarrow \frac{5|b+8|}{5}\gt \frac{20}{5}$
Simplify.
$\Rightarrow |b+8|\gt 4$
Write a compound inequality.
$\Rightarrow b+8\lt -4$ or $b+8\gt 4$
Subtract $8$ from each side.
$\Rightarrow b+8-8\lt -4-8$ or $b+8-8\gt 4-8$
Simplify.
$\Rightarrow b\lt -12$ or $b\gt -4$
Hence, the solution is $b\lt -12$ or $b\gt -4$.
