Question

Solve the linear equation: \(\frac{x-5}{3}=\frac{x-3}{5}\)

Answer 1

\(\frac{x-5}{3}=\frac{x-3}{5}\)
L.C.M. of the denominators, \(3\) and \(5\), is \(15\).
Multiplying both sides by \(15\), we obtain
\(5(x - 5) = 3(x - 3)\)
\(\Rightarrow\) \(5x - 25 = 3x - 9\) (Opening the brackets)
\(\Rightarrow\) \(5x - 3x = 25 - 9\)
\(\Rightarrow\) \(2x = 16\)
\(\Rightarrow\) \(x\) = \(\frac{16}{2}\)
\(\Rightarrow\) \(x = 8\)