Answer
$x=-\dfrac{5}{3}\text{ OR }x=3$
Work Step by Step
Using the properties of equality, the given equation, $
2|3x-2|=14
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{2|3x-2|}{2}=\dfrac{14}{2}
\\\\
|3x-2|=7
.\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}
3x-2=7
\\\\\text{OR}\\\\
3x-2=-7
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3x-2+2=7+2
\\
3x=9
\\
\dfrac{3x}{3}=\dfrac{9}{3}
\\
x=3
\\\\\text{OR}\\\\
3x-2+2=-7+2
\\
3x=-5
\\
\dfrac{3x}{3}=-\dfrac{5}{3}
\\
x=-\dfrac{5}{3}
.\end{array}
Hence, $
x=-\dfrac{5}{3}\text{ OR }x=3
.$
