Answer
the set of all real numbers
Work Step by Step
The given inequality, $
|-8-3x|-7\gt-8
,$ is equivalent to
\begin{array}{l}\require{cancel}
|-8-3x|\gt-8+7
\\\\
|-8-3x|\gt-1
.\end{array}
For any $x$, the left side of the inequality above is always a non negative number. This is always greater than the negative number at the right. Hence, the solution is $\text{
the set of all real numbers
.}$
