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

$\frac{3 \mathrm{x}+1}{16}+\frac{2 \mathrm{x}-3}{7}=\frac{\mathrm{x}+3}{8}+\frac{3 \mathrm{x}-1}{14}$

or $\frac{3 \mathrm{x}+1}{16}-\frac{\mathrm{x}+3}{8}=\frac{3 \mathrm{x}-1}{14}-\frac{2 \mathrm{x}-3}{7}$

or $\frac{3 \mathrm{x}+1-2 \mathrm{x}-6}{16}=\frac{3 \mathrm{x}-1-4 \mathrm{x}+6}{14}$

or $\frac{\mathrm{x}-5}{8}=\frac{-\mathrm{x}+5}{7}$

or $7 \mathrm{x}-35=-8 \mathrm{x}+40$

or $15 \mathrm{x}=75$

or $\mathrm{x}=\frac{75}{15}=5$

Check :

L.H.S. $=\frac{3 \times 5+1}{16}+\frac{2 \times 5-3}{7}=\frac{16}{16}+\frac{7}{7}=2$

R.H. S. $=\frac{5+3}{8}+\frac{3 \times 5-1}{14}=\frac{8}{8}+\frac{14}{14}=2$

$\therefore$ L.H.S. = R.H.S. for $x=5$