Question

Solve the linear equation: $m-\frac{m-1}{2}=1-\frac{m-2}{3}$

Answer 1

$m-\frac{m-1}{2}=1-\frac{m-2}{3}$
L.C.M. of the denominators, $2$ and $3$, is $6$.
Multiplying both sides by $6$, we obtain
$6m - 3(m - 1) = 6 - 2(m - 2)$
$\Rightarrow$ $6m - 3m + 3 = 6 - 2m + 4$ (Opening the brackets)
$\Rightarrow$ $6m - 3m + 2m = 6 + 4 - 3$
$\Rightarrow$ $5m = 7$
$\Rightarrow$ $m = \frac{7}{5}$