Question

Solve linear equation:
$m-\frac{m-1}{2}=1-\frac{m-2}{3}$.

• A. $m=\frac{4}{5}$
• B. $m=\frac{3}{5}$
• C. $m=\frac{8}{5}$
• D. $m=\frac{7}{5}$

Answer 1

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

Given, $m-\frac{m-1}{2}=1-\frac{m-2}{3}$.

Multiply both sides by $6$, we get,
$\Rightarrow$ $6(m-\frac{m-1}{2})=(1-\frac{m-2}{3})6$

$\Rightarrow$ $6m-3m+3=6-2m+4$ ...[By Distribution Law]

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

Transpose $2m$ to LHS and $3$ to RHS, we get,
$\Rightarrow$ $5m=7$

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

Hence, option $D$ is correct.