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

$\frac{1-2 \mathrm{x}}{7}-\frac{2-3 \mathrm{x}}{8}=\frac{3}{2}+\frac{\mathrm{x}}{4}$

or $\frac{1-2 \mathrm{x}}{7}=\frac{3}{2}+\frac{\mathrm{x}}{4}+\frac{2-3 \mathrm{x}}{8}$

or $\frac{1-2 \mathrm{x}}{7}=\frac{12+2 \mathrm{x}+2-3 \mathrm{x}}{8}$

or $\frac{1-2 \mathrm{x}}{7}=\frac{14-x}{8}$

or $8-16 \mathrm{x}=98-7 x$

or $-16 \mathrm{x}+7 \mathrm{x}=98-8$

or $\mathrm{x}=\frac{-90}{9}$

$=-10$

Check :

L. H. S. $=\frac{1-2 \times(-10)}{7}-\frac{2-3 \times(-10)}{8}=\frac{1+20}{7}-\frac{2+30}{8}=3-4=-1$

R.H.S. $=\frac{3}{2}+\frac{-10}{4}=\frac{3}{2}+\frac{-5}{2}=\frac{3-5}{2}=-1$

$\therefore$ L.H.S. $=$ R.H.S. for $x=-10$