Question

Solve the following linear equation:

$\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$

Answer 1

Compute the required value:

$\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$

On taking LCM on both sides and on solving, we get

$$\begin{gathered} \frac{5x-2}{10}=\frac{4x+3}{12} \\ \Rightarrow 12(5x-2)=10(4x+3) \\ \Rightarrow 60x-24=40x+30 \\ \Rightarrow 60x-40x=30+24 \\ \Rightarrow 20x=54 \\ \Rightarrow x=\frac{54}{20} \\ \Rightarrow x=\frac{27}{10} \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{27}}{\mathbf{10}}$ is the solution of given equation.