Answer
$x=\left\{ \dfrac{5}{4},\dfrac{5}{2} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|3x-5|=x
,$ use the definition of an absolute value equality.
$\bf{\text{Solution Details:}}$
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}
3x-5=x
\\\\\text{OR}\\\\
3x-5=-x
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3x-5=x
\\\\
3x-x=5
\\\\
2x=5
\\\\
x=\dfrac{5}{2}
\\\\\text{OR}\\\\
3x-5=-x
\\\\
3x+x=5
\\\\
4x=5
\\\\
x=\dfrac{5}{4}
.\end{array}
Hence, $
x=\left\{ \dfrac{5}{4},\dfrac{5}{2} \right\}
.$
