Answer
$\left( -\infty,0 \right)\cup(0,\infty)$
Work Step by Step
Since for any $a\gt0$, $|x|\ge a$ implies $x\ge a$ OR $x\le -a$, then the given inequality, $
|x|\gt0
,$ is equivalent to
\begin{array}{l}\require{cancel}
x\gt0
,\\\\\text{OR}\\\\
x\lt0
.\end{array}
Hence, the solution set is $
\left( -\infty,0 \right)\cup(0,\infty)
.$
See graph below.