## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x=\left\{ \dfrac{5}{4},\dfrac{5}{2} \right\}$
$\bf{\text{Solution Outline:}}$ 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, $x=\left\{ \dfrac{5}{4},\dfrac{5}{2} \right\} .$