Answer
$x=\left\{ -\dfrac{11}{2},\dfrac{13}{2} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\left| \dfrac{2x-1}{3} \right|=4
,$ use the definition of an absolute value equality. Then 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 given equation is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{2x-1}{3}=4
\\\\\text{OR}\\\\
\dfrac{2x-1}{3}=-4
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
\dfrac{2x-1}{3}=4
\\\\
3\cdot\dfrac{2x-1}{3}=3\cdot4
\\\\
2x-1=12
\\\\
2x=12+1
\\\\
2x=13
\\\\
x=\dfrac{13}{2}
\\\\\text{OR}\\\\
\dfrac{2x-1}{3}=-4
\\\\
3\cdot\dfrac{2x-1}{3}=3\cdot(-4)
\\\\
2x-1=-12
\\\\
2x=-12+1
\\\\
2x=-11
\\\\
x=-\dfrac{11}{2}
.\end{array}
Hence, $
x=\left\{ -\dfrac{11}{2},\dfrac{13}{2} \right\}
.$
