## Intermediate Algebra (12th Edition)

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 $\text{ the set of all real numbers .}$