Chapter 4 - Section 4.3 - Equations and Inequalities Involving Absolute Value - Exercise Set - Page 283: 42

$(-4,6)$

We are asked to solve the absolute value inequality: $|x-1|\lt 5$ We remove the absolute value sign by splitting the inequality into two as follows: $-5 \lt x-1 \lt 5$ We solve for $x$ by adding $1$: $-5+1 \lt x-1+1 \lt 5+1$ $-4 \lt x \lt 6$ In interval notation, this can be written as: $(-4,6)$ See the number line graph below.