Answer
$2\lt x \lt 8$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-1\lt x-3 \lt 5
.$ Then graph.
In the graph above, a hollowed dot is used for $\lt$ or $\gt$. A shaded dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
-1\lt x-3 \lt 5
\\\\
-1+3\lt x-3+3 \lt 5+3
\\\\
2\lt x \lt 8
.\end{array}
The graph includes the points from $2$ (exclusive) to $8$ (exclusive).
