# Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 138: 83

$(-\infty,-1]\cup[2,\infty)$

#### 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: $(-\infty,-1]\cup[2,\infty)$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.