Question

Solve the linear equation: \(m-\frac{m-1}{2}=1-\frac{m-2}{3}\)

Answer 1

\(m-\frac{m-1}{2}=1-\frac{m-2}{3}\)
L.C.M. of the denominators, \(2\) and \(3\), is \(6\).
Multiplying both sides by \(6\), we obtain
\(6m - 3(m - 1) = 6 - 2(m - 2)\)
\(\Rightarrow\) \(6m - 3m + 3 = 6 - 2m + 4\) (Opening the brackets)
\(\Rightarrow\) \(6m - 3m + 2m = 6 + 4 - 3\)
\(\Rightarrow\) \(5m = 7\)
\(\Rightarrow\) \(m = \frac{7}{5}\)