Solve each of the following equation and also verify your solution:

$\frac{2}{3}(\mathrm{x}-5)-\frac{1}{4}(\mathrm{x}-2)=\frac{9}{2}$

or $\frac{2 \mathrm{x}-10}{3}-\frac{\mathrm{x}-2}{4}=\frac{9}{2}$

or $\frac{8 \mathrm{x}-40-3 \mathrm{x}+6}{12}=\frac{9}{2}$

or $\frac{5 \mathrm{x}-34}{12}=\frac{9}{2}$

or $10 \mathrm{x}-68=108$

or $10 \mathrm{x}=108+68$

or $\mathrm{x}=\frac{176}{10}=\frac{88}{5}$

Verification :

L. H. S. $=\frac{2}{3}\left(\frac{88}{5}-5\right)-\frac{1}{4}\left(\frac{88}{5}-2\right)$

$=\frac{2}{3} \times \frac{63}{5}-\frac{1}{4} \times \frac{78}{5}=\frac{9}{2}=\mathrm{R} . \mathrm{H} . \mathrm{S} .$