Answer
$(-\infty,-1]\cup[2,\infty)$
Work Step by Step
Rewrite as
$|2x-1|\geq 3$
... $|u| \geq c $ is equivalent to ($ u\leq -c $) or ($ u \geq c $)
$ \begin{array}{lllll}
2x-1 \leq-3 & /+1 & ...or... & 2x-1\geq 3 & /+1\\
2x\leq-2 & /\div 2 & & 2x\geq 4 & /\div 2\\
x\leq-1 & & & x\geq 2 & \\
x\in(-\infty,-1] & & or & x\in[2,\infty) & \\
& & & &
\end{array}$
Solution set: $(-\infty,-1]\cup[2,\infty)$
