Answer
$q\lt -6$ or $q\gt -2$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow |2q+8|\gt 4$
Write a compound inequality.
$\Rightarrow 2q+8\lt -4$ or $2q+8\gt 4$
Subtract $8$ from each side.
$\Rightarrow 2q+8-8\lt -4-8$ or $2q+8-8\gt 4-8$
Simplify.
$\Rightarrow 2q\lt -12$ or $2q\gt -4$
Divide each side by $2$.
$\Rightarrow \frac{2q}{2}\lt \frac{-12}{2}$ or $\frac{2q}{2}\gt \frac{-4}{2}$
Simplify.
$\Rightarrow q\lt -6$ or $q\gt -2$
Hence, the solution is $q\lt -6$ or $q\gt -2$.
