Answer
$(-\infty, \infty)$
Work Step by Step
Using the properties of inequality, the given expression, $
9+|x|\gt7
,$ is equivalent to
\begin{array}{l}\require{cancel}
|x|\gt7-9
\\\\
|x|\gt-2
.\end{array}
The left side of the inequality, $
|x|\gt-2
,$ always gives a non-negative value. This is always greater than the value at the right. Hence, the solution set is $
(-\infty, \infty)
.$
