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

$x-2 x+2-\frac{16}{3} x+5=3-\frac{7}{2} x$

or $\frac{3 x-6 x+6-16 x+15}{3}=\frac{6-7 x}{2}$

or $\frac{-19 x+21}{3}=\frac{6-7 x}{2}$

or $-38 \mathrm{x}+42=18-21 \mathrm{x}$

or $-21 \mathrm{x}+38 \mathrm{x}=42-18$

or $17 \mathrm{x}=24$

or $\mathrm{x}=\frac{24}{17}$

Check:

L.H. S. $=\frac{24}{17}-2 \times \frac{24}{17}+7-\frac{16}{3} \times \frac{24}{17}=\frac{-33}{17}$

R.H.S. $=3-\frac{7}{2} \times \frac{24}{17}=\frac{-33}{17}$

$\therefore$ L.H.S. $=$ R.H.S. for $x=\frac{24}{17}$