#### Answer

$a=\left\{ -\dfrac{3}{5},5 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|3a-1|=|2a+4|
,$ use the definition of an absolute value equality. Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Since $|x|=|y|$ implies $x=y \text{ or } x=-y,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
3a-1=2a+4
\\\\\text{OR}\\\\
3a-1=-(2a+4)
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3a-1=2a+4
\\\\
3a-2a=4+1
\\\\
a=5
\\\\\text{OR}\\\\
3a-1=-(2a+4)
\\\\
3a-1=-2a-4
\\\\
3a+2a=-4+1
\\\\
5a=-3
\\\\
a=-\dfrac{3}{5}
.\end{array}
Hence, $
a=\left\{ -\dfrac{3}{5},5 \right\}
.$