Answer
Interval: $(- \frac{15}{2},\ -7)\cup\ (-7,\ -\frac{13}{2})$
Work Step by Step
$\frac{1}{|x+7|}\gt 2$
We can see that $x\neq -7$ because otherwise we would have division by 0.
$1\gt 2|x+7|$
$\frac{1}{2}\gt |x+7|$
$|x+7|\lt \frac{1}{2}$
$-\frac{1}{2}\lt x+7\lt \frac{1}{2}$
$-\frac{15}{2}\lt x\lt -\frac{13}{2}$
We use interval notation and skip $x=-7$:
Interval: $(- \frac{15}{2},\ -7)\cup\ (-7,\ -\frac{13}{2})$
