Solve each of the following equation and also check your result in each case:

$x-\frac{(x-1)}{2}=1-\frac{(x-2)}{3}$

or $\frac{2 \mathrm{x}-\mathrm{x}+1}{2}=\frac{3-\mathrm{x}+2}{3}$

or $\frac{\mathrm{x}+1}{2}=\frac{5-\mathrm{x}}{3}$

or $3 \mathrm{x}+3=10-2 \mathrm{x}$

or $5 \mathrm{x}=10-3$

or $\mathrm{x}=\frac{7}{5}$

Check :

L. H.S. $=\frac{7}{5}-\frac{\frac{7}{5}-1}{2}=\frac{7}{5}-\frac{1}{5}=\frac{6}{5}$

R.H.S. $=1-\frac{\frac{7}{5}-2}{3}=1-\frac{-3}{15}=\frac{6}{5}$

$\therefore$ L.H.S. $=$ R.H.S. for $x=\frac{7}{5}$