Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 55

$(-\infty,-1)\cup(2,\infty)$ See graph.

Step 1. $|1-2x|\gt|-3|$ or $|2x-1|\gt3$ can be separated into $2x-1\gt3$ or $2x-1\lt-3$ which lead to $x\gt2$ or $x\lt-1$, thus we have the solution $(-\infty,-1)\cup(2,\infty)$ Step 2. See graph.