#### Answer

Choice E

#### Work Step by Step

Since for any $a\gt0$, $|x|\gt a$ implies $x\gt a$ or $x\lt-a$, then the given inequality, $
|x|\gt7
,$ is equivalent to
\begin{array}{l}\require{cancel}
x\gt7
\\\\\text{OR}\\\\
x\lt-7
.\end{array}
Hence, the graph is $\text{
Choice E
}.$