Answer
$(-\infty, -5) \cup (1, +\infty)$
Refer to the image below for the graph.
Work Step by Step
RECALL:
$|x| \gt a \longrightarrow x \gt a \text{ or } x \lt -a$
Use the rule above to obtain:
$2+x \gt 3 \color{blue}{\text{ or }} 2+x \lt -3$
Solve each inequality to obtain:
$2+x\gt 3
\\x \gt 3-2
\\x \gt 1$
or
$2+x \lt -3
\\x \lt -3-2
\\x \lt -5$
In interval notation, the solution set is:
$(-\infty, -5) \cup (1, +\infty)$
To graph the inequalities, plot holes at $-5$ and $1$, then shade the region to the right of $1$ and the region to the left of $-5$.
