Answer
$x=\left\{ \dfrac{7}{3},3 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|8-3x|-3=-2
,$ use the properties of equality to isolate the absolute value expression. Then use the properties of absolute value equality.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
|8-3x|=-2+3
\\\\
|8-3x|=1
.\end{array}
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}
8-3x=1
\\\\\text{OR}\\\\
8-3x=-1
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
8-3x=1
\\\\
-3x=1-8
\\\\
-3x=-7
\\\\
x=\dfrac{-7}{-3}
\\\\
x=\dfrac{7}{3}
\\\\\text{OR}\\\\
8-3x=-1
\\\\
-3x=-1-8
\\\\
-3x=-9
\\\\
x=\dfrac{-9}{-3}
\\\\
x=3
.\end{array}
Hence, $
x=\left\{ \dfrac{7}{3},3 \right\}
.$
