Question

Solve the linear equation:

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

• A. $m=\frac{7}{2}$
• B. $m=\frac{3}{4}$
• C. $m=\frac{7}{5}$
• D. $m=\frac{4}{7}$

Answer 1

The correct option is C $m=\frac{7}{5}$

We have $m-\frac{m-1}{2}=1-\frac{m-2}{3}$

$\Rightarrow \frac{2m-m+1}{2}=\frac{3-m+2}{3}$ ....[Taking LCM on LHS and RHS]

$\Rightarrow \frac{m+1}{2}=\frac{5-m}{3}$

$\Rightarrow 3(m+1)=2(5-m)$ ....[By\quad cross-multiplication]

$\Rightarrow 3m+3=10-2m$

$\Rightarrow 3m+2m=10-3$ ....[Transposing $3$ to RHS and $-2m$ to LHS]

$\Rightarrow 5m=7$

$\Rightarrow m=\frac{7}{5}$