#### Answer

$E$

#### Work Step by Step

RECALL:
$|x| \gt a \longrightarrow x \gt a \text{ or } x \lt -a$
Using the rule above gives:
$|x| \gt 7 \longrightarrow x \gt 7 \text{ or } x\lt -7$
Thus, the solutions to the given inequality are the numbers that are either greater than $7$ or less than $-7$.
The graph that represents these numbers is the one in Option $E$.