#### Answer

$(-\infty,-4)\cup (-2,\infty)$

#### Work Step by Step

We are asked to solve the absolute value inequality:
$|x+3|\gt 1$
We remove the absolute value sign by splitting the inequality into two as follows:
$x+3 \lt -1$ or $x+3 \gt 1$
Now, we solve for (isolate) $x$:
$x+3-3 \lt -1-3$ or $x+3-3 \gt 1-3$
$x \lt -4$ or $x \gt -2$
In interval notation, this can be written as:
$(-\infty,-4)\cup (-2,\infty)$
See the number line graph below.