Question

Solve the following linear equation:

$m-\frac{(m-1)}{2}=1-\frac{(m-2)}{3}$

Answer 1

Given :

$m-\frac{(m-1)}{2}=1-\frac{(m-2)}{3}$

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

$$\begin{gathered} \frac{2m-(m-1)}{2}=\frac{3-(m-2)}{3} \\ \Rightarrow \frac{2m-m+1}{2}=\frac{3-m+2}{3} \\ \Rightarrow \frac{m+1}{2}=\frac{5-m}{3} \\ \Rightarrow 3(m+1)=2(5-m) \\ \Rightarrow 3m+3=10-2m \\ \Rightarrow 3m+2m=10-3 \\ \Rightarrow 5m=7 \\ \Rightarrow m=\frac{7}{5} \end{gathered}$$

Hence, $\mathit{m}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{7}}{\mathbf{5}}$ is the solution of given equation.