#### Answer

$m=-3$

#### Work Step by Step

Multiplying both sides by the $LCD=
2
$, then the solution to the given equation, $
\dfrac{1}{2}+4m=3m-\dfrac{5}{2}
$, is
\begin{array}{l}
1(1)+2(4m)=2(3m)-1(5)
\\\\
1+8m=6m-5
\\\\
8m-6m=-5-1
\\\\
2m=-6
\\\\
m=-\dfrac{6}{2}
\\\\
m=-3
.\end{array}
CHECKING:
\begin{array}{l}
\dfrac{1}{2}+4(-3)=3(-3)-\dfrac{5}{2}
\\\\
\dfrac{1}{2}-12=-9-\dfrac{5}{2}
\\\\
\dfrac{1}{2}-\dfrac{24}{2}=-\dfrac{18}{2}-\dfrac{5}{2}
\\\\
-\dfrac{23}{2}=-\dfrac{23}{2}
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
m=-3
$.