Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 53

$(-1,\frac{3}{2})$ See graph.

Step 1. $|1-4x|-7\lt-2$ or $|4x-1|\lt5$ can be separated into $-5\lt 4x-1\lt5 \longrightarrow -4\lt 4x\lt6 \longrightarrow -1\lt x\lt\frac{3}{2}$, thus we have the solution $(-1,\frac{3}{2})$ Step 2. See graph.