Solve for: |2m+7|=6m+13

Expression: $|2m+7|=6m+13$

Move the variable to the left-hand side and change its sign

$|2m+7|-6m=13$

Separate the equation into $2$ possible cases

$\begin{array} { l }\begin{array} { l }2m+7-6m=13,& 2m+7 \geq 0\end{array},\\\begin{array} { l }-\left( 2m+7 \right)-6m=13,& 2m+7 < 0\end{array}\end{array}$

Solve the equation for $m$

$\begin{array} { l }\begin{array} { l }m=-\frac{ 3 }{ 2 },& 2m+7 \geq 0\end{array},\\\begin{array} { l }-\left( 2m+7 \right)-6m=13,& 2m+7 < 0\end{array}\end{array}$

Solve the inequality for $m$

$\begin{array} { l }\begin{array} { l }m=-\frac{ 3 }{ 2 },& m \geq -\frac{ 7 }{ 2 }\end{array},\\\begin{array} { l }-\left( 2m+7 \right)-6m=13,& 2m+7 < 0\end{array}\end{array}$

Solve the equation for $m$

$\begin{array} { l }\begin{array} { l }m=-\frac{ 3 }{ 2 },& m \geq -\frac{ 7 }{ 2 }\end{array},\\\begin{array} { l }m=-\frac{ 5 }{ 2 },& 2m+7 < 0\end{array}\end{array}$

Solve the inequality for $m$

$\begin{array} { l }\begin{array} { l }m=-\frac{ 3 }{ 2 },& m \geq -\frac{ 7 }{ 2 }\end{array},\\\begin{array} { l }m=-\frac{ 5 }{ 2 },& m < -\frac{ 7 }{ 2 }\end{array}\end{array}$

Find the intersection

$\begin{array} { l }m=-\frac{ 3 }{ 2 },\\\begin{array} { l }m=-\frac{ 5 }{ 2 },& m < -\frac{ 7 }{ 2 }\end{array}\end{array}$

Find the intersection

$\begin{array} { l }m=-\frac{ 3 }{ 2 },\\∅\end{array}$

Find the union

$\begin{align*}&m=-\frac{ 3 }{ 2 } \\&\begin{array} { l }m=-1 \frac{ 1 }{ 2 },& m=-1.5\end{array}\end{align*}$