Answer
$(1,3)$
Work Step by Step
We are asked to solve the absolute value inequality:
$|x-2|\lt 1$
We remove the absolute value sign by splitting the inequality into two as follows:
$-1 \lt x-2 \lt 1$
We solve for $x$ by adding $2$:
$-1+2 \lt x-2+2 \lt 1+2$
$1 \lt x \lt 3$
In interval notation, this can be written as:
$(1,3)$
See the number line graph below.
