Answer
$x=\{-4,14\}$
Work Step by Step
Since for any nonnegative number $c$, $|x|=c$ implies $x=c \text{ OR } x=-c$, then the values that satisfy the given equation, $
|x-5|=9
,$ are
\begin{array}{l}\require{cancel}
x-5=9
\\\\
x=9+5
\\\\
x=14
\\\\\text{ OR }\\
x-5=-9
\\\\
x=-9+5
\\\\
x=-4
.\end{array}
Hence, $
x=\{-4,14\}
.$
