Question

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

Answer 1

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

$⟹$ $\frac{2m-\left(m-1\right)}{2}=\frac{3-\left(m-3\right)}{3}$ ...[Taking LCM of the denominators]

$⟹$ $\frac{2m-m+1}{2}=\frac{3-m+3}{3}$ ...{By distribution property]

$⟹$ $\frac{m+1}{2}=\frac{6-m}{3}$ ...[On simplifying]

$⟹$ $3\left(m+1\right)=2\left(6-m\right)$ …[Cross-multiplying the denominators]

$⟹$ $3m+3=12-2m$ ...{By distribution property]

$⟹$ $3m+2m=12-3$ ...[Transposing $x$ terms to one side]

$⟹$ $5m=9$

$⟹$ $m=\frac{9}{5}$.