Question

Question 6
$m-\frac{m-1}{2}=1-\frac{m-2}{3}$

Answer 1

$m-\frac{m-1}{2}=1-\frac{m-2}{3}$
$\Rightarrow \frac{2m-m+1}{2}=\frac{3-m+2}{3}$
$\Rightarrow \frac{m+1}{2}=\frac{5-m}{3}$
$\Rightarrow 3(m+1)=2(5-m)$
$\Rightarrow 3m+3=10-2m$
$\Rightarrow 3m+2m=10-3$
$\Rightarrow 5m=7$
$\Rightarrow m=\frac{7}{5}$

$\Rightarrow \text{Check:}$

$\Rightarrow$$\frac{7}{5}-\frac{\frac{7}{5}-1}{2}$ = 1-$\frac{\frac{7}{5}-2}{3}$

$\Rightarrow \frac{7}{5}-\frac{\frac{7-5}{5}}{2}=1-\frac{\frac{7-10}{5}}{3}\Rightarrow \frac{7}{5}-\frac{2}{5\times 2}=1-\frac{-3}{5\times 3}$

$\Rightarrow \frac{7}{5}-\frac{1}{5}=1+\frac{1}{5}\Rightarrow \frac{7-1}{5}=\frac{5+1}{5}$

$\Rightarrow \frac{6}{5}=\frac{6}{5}$

$\Rightarrow L.H.S.=R.H.S$

Therefore, it is correct