Question

Solve: $m-\frac{(m-1)}{2}=1-\frac{(m-2)}{3}$.

Answer 1

Given $m-\frac{(m-1)}{2}=1-\frac{(m-2)}{3}$
take LCM on both sides
$\Rightarrow \frac{2m-m+1}{2}=\frac{3-m+2}{3}$
$\Rightarrow \frac{m+1}{2}=\frac{5-m}{3}$
$\Rightarrow 3(m+1)=2(5-m)$ [Cross Multiplying]
$\Rightarrow 3m+3=10-2m$
$\Rightarrow 3m+2m=10-3$
$\Rightarrow 5m=7$
$\therefore m=\frac{7}{5}$