Question

Solve each of the following equation and also check your result in each case:
$\frac{9x+7}{2}-\left(x-\frac{x-2}{7}\right)=36$

Answer 1

$$\begin{gathered} \frac{9\mathrm{x}+7}{2}-(\mathrm{x}-\frac{\mathrm{x}-2}{7})=36 \\ \mathrm{or}\frac{63\mathrm{x}+49-14\mathrm{x}+2\mathrm{x}-4}{14}=36 \\ \mathrm{or}\frac{51\mathrm{x}+45}{14}=36 \\ \mathrm{or}51\mathrm{x}+45=504 \\ \mathrm{or}51\mathrm{x}=504-45 \\ \mathrm{or}\mathrm{x}=\frac{459}{51}=9 \\ \mathrm{Thus},\mathrm{x}=9\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{x}=9\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{9\times 9+7}{2}-(9-\frac{9-2}{7})=\frac{88}{2}-9+\frac{7}{7}=44-9+1=36 \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=36 \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=9. \end{gathered}$$