Answer
$(-\displaystyle \infty,-\frac{11}{5}) \cup (3, \infty)$
Work Step by Step
The solutions of $|u|\gt c $ are the numbers that satisfy $ u\lt -c $ or $ u\gt c.$
---
$|5x-2| \gt 13\Rightarrow \left\{\begin{array}{ll}
5x-2\lt -13 & \\
or & \\
5x-2 \gt 13 &
\end{array}\right.$
$ \begin{array}{lllll}
5x-2\lt -13 & /+2 & ...or... & 5x-2 \gt 13 & /+2\\
5x\lt -11 & /\div 5 & & 5x \gt 15 & /\div 5\\
x\lt -11/5 & & & x \gt 3 & \\
x\in(-\infty,-11/5) & & or & x\in(3,\infty) & \\
& & & &
\end{array} $
Solution set: $(-\displaystyle \infty,-\frac{11}{5}) \cup (3, \infty)$
