Question

Solve: $\frac{3}{7}\mathrm{x}=\frac{20}{7}-\mathrm{x}$

Answer 1

Given equation: $\frac{3}{7}\mathrm{x}=\frac{20}{7}-\mathrm{x}$

Transposing $-\mathrm{x}$ to the L.H.S. (left hand side) of the equation,

$$\begin{gathered} \Rightarrow \frac{3}{7}\mathrm{x}+\mathrm{x}=\frac{20}{7} \\ \Rightarrow \frac{3\mathrm{x}+7\mathrm{x}}{7}=\frac{20}{7} \\ \Rightarrow \frac{10\mathrm{x}}{7}=\frac{20}{7} \end{gathered}$$

Now divide both side of the equation by $\frac{7}{10}$,

$$\begin{gathered} \Rightarrow \frac{10\mathrm{x}}{7}\times \frac{7}{10}=\frac{20}{7}\times \frac{7}{10} \\ \Rightarrow \frac{\cancel{10}\mathrm{x}}{\cancel{7}}\times \frac{\cancel{7}}{\cancel{10}}=\frac{{\displaystyle \stackrel{2}{\cancel{20}}}}{\cancel{7}}\times \frac{\cancel{7}}{\cancel{10}} \\ \Rightarrow \mathrm{x}=2 \end{gathered}$$

Hence, $\mathrm{x}=2$ is the solution of the given equation.