$$\frac { 2 m - 3 } { 2 } - \frac { m + 1 } { 3 } = \frac { 3 m - 8 } { 4 }$$
$m=2$
$$6\left(2m-3\right)-4\left(m+1\right)=3\left(3m-8\right)$$
$$12m-18-4\left(m+1\right)=3\left(3m-8\right)$$
$$12m-18-4m-4=3\left(3m-8\right)$$
$$8m-18-4=3\left(3m-8\right)$$
$$8m-22=3\left(3m-8\right)$$
$$8m-22=9m-24$$
$$8m-22-9m=-24$$
$$-m-22=-24$$
$$-m=-24+22$$
$$-m=-2$$
$$m=2$$
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