Answer
$(1,5)$
Work Step by Step
Since $|x|\lt c$ implies $-c\lt x\lt c,$ then the solution to the given inequality, $
|x-3|\lt2
,$ is equivalent to
\begin{array}{l}\require{cancel}
-2\lt x-3\lt2
\\\\
-2+3\lt x-3+3\lt2+3
\\\\
1\lt x\lt5
.\end{array}
The graph of the solution set is shown below.
In interval notation, this is equivalent $
(1,5)
.$