Question

Solve the linear equation \(\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}\)

Answer 1

\(\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}\)
L.C.M. of the denominators, \(2, 3, 4\), and \(5\), is \(60\).
Multiplying both sides by \(60\), we obtain 

\(60\bigg(\frac{x}{2}-\frac{1}{5}\bigg)=60\bigg(\frac{x}{3}+\frac{1}{4}\bigg)\)

\(\Rightarrow\) \(30x - 12\) = \(20x + 15 \) (Opening the brackets)
\(\Rightarrow\) \(30x - 20x\) = \(15 + 12\)
\(\Rightarrow\) \(10x = 27\)
\(\Rightarrow\) \(x = \frac{27}{10}\)