Question

Solve each of the following equation and also verify your solution:
$\frac{2}{3}(x-5)-\frac{1}{4}(x-2)=\frac{9}{2}$

Answer 1

$$\begin{gathered} \frac{2}{3}(\mathrm{x}-5)-\frac{1}{4}(\mathrm{x}-2)=\frac{9}{2} \\ \mathrm{or}\frac{2\mathrm{x}-10}{3}-\frac{\mathrm{x}-2}{4}=\frac{9}{2} \\ \mathrm{or}\frac{8\mathrm{x}-40-3\mathrm{x}+6}{12}=\frac{9}{2} \\ \mathrm{or}\frac{5\mathrm{x}-34}{12}=\frac{9}{2} \\ \mathrm{or}10\mathrm{x}-68=108 \\ \mathrm{or}10\mathrm{x}=108+68 \\ \mathrm{or}\mathrm{x}=\frac{176}{10}=\frac{88}{5} \\ \mathrm{Verification}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{2}{3}(\frac{88}{5}-5)-\frac{1}{4}(\frac{88}{5}-2) \\ =\frac{2}{3}\times \frac{63}{5}-\frac{1}{4}\times \frac{78}{5}=\frac{9}{2}=\mathrm{R}.\mathrm{H}.\mathrm{S}. \end{gathered}$$