Answer
$\text{the interval } \left( -\infty,-7 \right]\cup \left[ 17,\infty \right)
$
Work Step by Step
Since $|x|\gt a$ implies $x\gt a \text{ OR } x\lt -a$, then the statement $
|x-5|\ge12
$ evaluates to
\begin{array}{l}
x-5\ge12\\
x\ge17
,\\\\\text{OR}\\\\
x-5\le-12\\
x\le-7
.\end{array}
Hence, the solution set is $
\text{the interval } \left( -\infty,-7 \right]\cup \left[ 17,\infty \right)
$.
