Answer
$\left( -\infty, -2 \right)
\cup
\left( 8,\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|3-x|\gt5
,$ use the definition of absolute value inequalities. Then use the properties of inequality to isolate the variable.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|\gt c$ implies $x\gt c \text{ or } x\lt-c$ (which is equivalent to $|x|\ge c$ implies $x\ge c \text{ or } x\le-c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
3-x\gt5
\\\\\text{OR}\\\\
3-x\lt-5
.\end{array}
Using the properties of inequality to isolate the variable results to
\begin{array}{l}\require{cancel}
-x\gt5-3
\\\\
-x\gt2
\\\\\text{OR}\\\\
3-x\lt-5
\\\\
-x\lt-5-3
\\\\
-x\lt-8
.\end{array}
Dividing by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-x\gt2
\\\\
x\lt\dfrac{2}{-1}
\\\\
x\lt-2
\\\\\text{OR}\\\\
-x\lt-8
\\\\
x\gt\dfrac{-8}{-1}
\\\\
x\gt8
.\end{array}
In interval notation, the solution set is $
\left( -\infty, -2 \right)
\cup
\left( 8,\infty \right)
.$
The colored graph is the graph of the solution set.