Answer
$x=\{ 2,4 \}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|9-3x|=3
,$ use the definition of absolute value equality. Use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
9-3x=3
\\\\\text{OR}\\\\
9-3x=-3
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
9-3x=3
\\\\
-3x=3-9
\\\\
-3x=-6
\\\\
x=\dfrac{-6}{-3}
\\\\
x=2
\\\\\text{OR}\\\\
9-3x=-3
\\\\
-3x=-3-9
\\\\
-3x=-12
\\\\
x=\dfrac{-12}{-3}
\\\\
x=4
.\end{array}
Hence, $
x=\{ 2,4 \}
.$
The colored points is the graph of the solution set.