Answer
$x=-6\text{ OR }x=12$
Work Step by Step
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation, $
|x-3|=9
,$ is equivalent to
\begin{array}{l}\require{cancel}
x-3=9
\\\\\text{OR}\\\\
x-3=-9
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x-3=9
\\
x-3+3=9+3
\\
x=12
\\\\\text{OR}\\\\
x-3=-9
\\
x-3+3=-9+3
\\
x=-6
.\end{array}
Hence, $
x=-6\text{ OR }x=12
.$
