Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 60

$ (\frac{47}{16}, \frac{49}{16})$ See graph.

Step 1. $|(4x-1)-11|\lt \frac{1}{4}\longrightarrow |4x-12|\lt \frac{1}{4} \longrightarrow |x-3|\lt \frac{1}{16}$ can be separated into $-\frac{1}{16}\lt x-3\lt \frac{1}{16} \longrightarrow \frac{47}{16}\lt x\lt \frac{49}{16}$, thus we have the solution $ (\frac{47}{16}, \frac{49}{16})$ Step 2. See graph.