#### Answer

$(-4,6)$

#### Work Step by Step

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.