Answer
$(-\displaystyle \infty,\frac{1}{3}) \cup(5,\infty)$
Work Step by Step
The solutions of $|u|\gt c $ are the numbers that satisfy $ u\lt -c $ or $ u\gt c.$
---
$|3x-8| \gt 7\Rightarrow \left\{\begin{array}{ll}
3x-8\lt -7 & \\
or & \\
x-1 \gt 7 &
\end{array}\right.$
$ \begin{array}{lllll}
3x-8\lt -7 & /+8 & ...or... & 3x-8 \gt 7 & /+8\\
3x\lt 1 & /\div 3 & & 3x \gt 15 & /\div 3\\
x\lt 1/3 & & & x \gt 5 & \\
x\in(-\infty,1/3) & & or & x\in(5,\infty) & \\
& & & &
\end{array} $
Solution set: $(-\displaystyle \infty,\frac{1}{3}) \cup(5,\infty)$
