Question

Solve the following equation and verify your answer:
$\frac{2x-(7-5x)}{9x-(3+4x)}=\frac{7}{6}$

Answer 1

$$\begin{gathered} \frac{2\mathrm{x}-(7-5\mathrm{x})}{9\mathrm{x}-(3+4\mathrm{x})}=\frac{7}{6} \\ \mathrm{or}\frac{7\mathrm{x}-7}{5\mathrm{x}-3}=\frac{7}{6} \\ \mathrm{or}42\mathrm{x}-42=35\mathrm{x}-21[\text{After c}\mathrm{ross}\mathrm{multipl}\text{ication}] \\ \mathrm{or}42\mathrm{x}-35\mathrm{x}=-21+42 \\ \mathrm{or}7\mathrm{x}=21 \\ \mathrm{or}\mathrm{x}=\frac{21}{7} \\ \mathrm{or}\mathrm{x}=3 \\ \mathrm{Thus},\mathrm{x}=3\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{x}=3\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{2\times 3-(7-5\times 3)}{9\times 3-(3+4\times 3)}=\frac{6-(7-15)}{27-(3+12)}=\frac{6+8}{27-15}=\frac{14}{12}=\frac{7}{6} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{7}{6} \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=3. \end{gathered}$$