Question

Solve for m: $m-\frac{m-1}{2}=1-\frac{m-2}{3}$

Answer 1

$\begin{array}{c}Wehave\\ m-\frac{m-1}{2}=1-\frac{m-2}{3}\\ \Rightarrow \frac{2m-m+1}{2}=\frac{3-m+2}{3}\\ \Rightarrow \frac{m+1}{2}=\frac{5-m}{3}\\ \Rightarrow 3\left(m+1\right)=2\left(5-m\right)\\ \Rightarrow 3m+3=10-2m\\ \Rightarrow 3m+2m=10-3\\ \Rightarrow 5m=7\\ \therefore m=\frac{7}{5}\\ Hence,thevalueofmis\frac{7}{5}.\end{array}$