Solve each of the following equation and also verify your solution:
$\frac{2}{3}(x-5)-\frac{1}{4}(x-2)=\frac{9}{2}$
$\frac{2}{3}(\mathrm{x}-5)-\frac{1}{4}(\mathrm{x}-2)=\frac{9}{2}$
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. $=\frac{2}{3}\left(\frac{88}{5}-5\right)-\frac{1}{4}\left(\frac{88}{5}-2\right)$
$=\frac{2}{3} \times \frac{63}{5}-\frac{1}{4} \times \frac{78}{5}=\frac{9}{2}=\mathrm{R} . \mathrm{H} . \mathrm{S} .$
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