Answer
$x\lt -10$ or $x\gt6$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow |2x+4|\gt16$
Write a compound inequality.
$\Rightarrow 2x+4\lt -16$ or $2x+4\gt16$
Subtract $4$ from each side.
$\Rightarrow 2x+4-4\lt -16-4$ or $2x+4-4\gt16-4$
Simplify.
$\Rightarrow 2x\lt -20$ or $2x\gt12$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}\lt \frac{-20}{2}$ or $\frac{2x}{2}\gt\frac{12}{2}$
Simplify.
$\Rightarrow x\lt -10$ or $x\gt6$
Hence, the solution is $x\lt -10$ or $x\gt6$.
