Question

Solve the following equations:

$2\mathrm{x}-\frac{1}{3}=\frac{2}{3}\mathrm{x}+4$

Answer 1

Given : $2\mathrm{x}-\frac{1}{3}=\frac{2}{3}\mathrm{x}+4$

On transposing $-\frac{1}{3}$ to the right and $\frac{2}{3}\mathrm{x}$ to the left

$$\begin{gathered} \Rightarrow 2\mathrm{x}-\frac{2}{3}\mathrm{x}=\frac{1}{3}+4 \\ \Rightarrow \frac{6\mathrm{x}-2\mathrm{x}}{3}=\frac{1+12}{3} \\ \Rightarrow \frac{4\mathrm{x}}{3}=\frac{13}{3} \end{gathered}$$

Multiply both side of the equation by $\frac{3}{4}$,

$$\begin{gathered} \Rightarrow \frac{4\mathrm{x}}{3}\times \frac{3}{4}=\frac{13}{3}\times \frac{3}{4} \\ \Rightarrow \frac{\cancel{4}\mathrm{x}}{\cancel{3}}\times \frac{\cancel{3}}{\cancel{4}}=\frac{13}{\cancel{3}}\times \frac{\cancel{3}}{4} \\ \Rightarrow \mathrm{x}=\frac{13}{4} \\ \Rightarrow \mathrm{x}=3\frac{1}{4} \end{gathered}$$

Hence, $\mathrm{x}=3\frac{1}{4}$ is the solution of the given equation.