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

$\frac{3 a-2}{3}+\frac{2 a+3}{2}=a+\frac{7}{6}$

or $\frac{6 \mathrm{a}-4+6 \mathrm{a}+9}{6}=\mathrm{a}+\frac{7}{6}$

or $12 \mathrm{a}+5=6 \mathrm{a}+7$

or $6 \mathrm{a}=7-5$

or $\mathrm{a}=\frac{2}{6}=\frac{1}{3}$

Check :

L.H.S. $=\frac{3 \times \frac{1}{3}-2}{3}+\frac{2 \times \frac{1}{3}+3}{2}=\frac{-1}{3}+\frac{11}{6}=\frac{9}{6}=\frac{3}{2}$

R.H. S. $=\frac{1}{3}+\frac{7}{6}=\frac{9}{6}=\frac{3}{2}$

$\therefore$ L.H.S. $=$ R.H.S. for $a=\frac{1}{3}$