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

$\frac{3 x}{4}-\frac{(x-1)}{2}=\frac{(x-2)}{3}$

or $\frac{3 x-2 x+2}{4}=\frac{x-2}{3}$

or $4 x-8=3 x+6$

or $x=14$

Check:

L. H.S. $=\frac{3 \times 14}{4}-\frac{14-1}{2}=\frac{21}{2}-\frac{13}{2}=\frac{8}{2}=4$

R.H.S. $=\frac{14-2}{3}=\frac{12}{3}=4$

Check:

L. H.S. $=\frac{3 \times 14}{4}-\frac{14-1}{2}=\frac{21}{2}-\frac{13}{2}=\frac{8}{2}=4$

R.H.S. $=\frac{14-2}{3}=\frac{12}{3}=4$

$\therefore$ L.H.S. $=$ R.H.S. for $x=14$