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

$\frac{6 x+1}{2}+1=\frac{7 x-3}{3}$

or $\frac{6 \mathrm{x}+1+2}{2}=\frac{7 \mathrm{x}-3}{3}$

or $18 \mathrm{x}+9=14 \mathrm{x}-6$

or $18 \mathrm{x}-14 \mathrm{x}=-6-9$

or $4 \mathrm{x}=-15$

or $\mathrm{x}=\frac{-15}{4}$

Check :

L. H.S. $=\frac{6 \times \frac{-15}{4}+1}{2}+1=\frac{-45+2+4}{4}=\frac{-39}{4}$

R. H.S. $=\frac{7 \times \frac{-15}{4}-3}{3}=\frac{-105-12}{12}=\frac{-39}{4}$

$\therefore$ L.H.S. $=$ R.H.S. for $x=\frac{-15}{4}$