Answer
$x=\left\{ -\dfrac{8}{5},7 \right\}$
Work Step by Step
Using the properties of absolute value, the given equation, $
|6x+1|=|15+4x|
,$ is equivalent to
\begin{array}{l}\require{cancel}
6x+1=15+4x
\\\text{ and } \\
6x+1=-(15+4x)
.\end{array}
Using the properties of equality, then
\begin{array}{l}\require{cancel}
6x+1=15+4x
\\
6x-4x=15-1
\\
2x=14
\\
x=\dfrac{14}{2}
\\
x=7
\\\\\text{ and } \\\\
6x+1=-(15+4x)
\\
6x+1=-15-4x
\\
6x+4x=-15-1
\\
10x=-16
\\
x=-\dfrac{16}{10}
\\
x=-\dfrac{8}{5}
.\end{array}
Hence, the solution set is $
x=\left\{ -\dfrac{8}{5},7 \right\}
.$