Answer
$\text{the interval } \left( -\infty,-24 \right]\cup \left[ 16,\infty \right)
$
Work Step by Step
Since $|x|\gt a$ implies $x\gt a \text{ OR } x\lt -a$, then the statement $
|x+4|\ge20
$ evaluates to
\begin{array}{l}
x+4\ge20\\
x\ge16
,\\\\\text{OR}\\\\
x+4\le-20\\
x\le-24
.\end{array}
Hence, the solution set is $
\text{the interval } \left( -\infty,-24 \right]\cup \left[ 16,\infty \right)
$.
