Answer
$x=\left\{ -\dfrac{14}{5},\dfrac{22}{5}, \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\left| \dfrac{4-5x}{6} \right|=3
,$ 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{4-5x}{6}=3
\\\\\text{OR}\\\\
\dfrac{4-5x}{6}=-3
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
\dfrac{4-5x}{6}=3
\\\\
6\cdot\dfrac{4-5x}{6}=6\cdot3
\\\\
4-5x=18
\\\\
-5x=18-4
\\\\
-5x=14
\\\\
x=\dfrac{14}{-5}
\\\\
x=-\dfrac{14}{5}
\\\\\text{OR}\\\\
\dfrac{4-5x}{6}=-3
\\\\
6\cdot\dfrac{4-5x}{6}=6\cdot(-3)
\\\\
4-5x=-18
\\\\
-5x=-18-4
\\\\
-5x=-22
\\\\
x=\dfrac{-22}{-5}
\\\\
x=\dfrac{22}{5}
.\end{array}
Hence, $
x=\left\{ -\dfrac{14}{5},\dfrac{22}{5}, \right\}
.$