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

$6.5 \mathrm{x}+\frac{19.5 \mathrm{x}-32.5}{2}=6.5 \mathrm{x}+13+\frac{13 \mathrm{x}-26}{2}$

or $\frac{19.5 x-32.5}{2}-\frac{13 x-26}{2}=13$

or $\frac{19.5 \mathrm{x}-32.5-13 \mathrm{x}+26}{2}=13$

or $6.5 \mathrm{x}-6.5=26[$ After $c$ ross multiplication $]$

or $6.5 \mathrm{x}=26+6.5$

or $\mathrm{x}=\frac{32.5}{6.5}=5$

Thus, $x=5$ is the solution of the given equation.

Check:

Substituting $x=5$ in the given equation, we get:

L.H. S. $=6.5 \times 5+\frac{19.5 \times 5-32.5}{2}=65$

R.H.S. $=6.5 \times 5+13+\frac{13 \times 5-26}{2}=65$

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