Question

Solve for $x$:

$\frac{x}{2}-\frac{1}{4}=\frac{x}{3}+\frac{1}{2}$

Answer 1

Given, $\frac{x}{2}-\frac{1}{4}=\frac{x}{3}+\frac{1}{2}$

$⟹$ $\frac{x}{2}-\frac{x}{3}=\frac{1}{2}+\frac{1}{4}$ ....(Transposing $\frac{x}{3}$ to LHS and $\frac{1}{4}$ to RHS)

$⟹$ $\frac{3x-2x}{6}=\frac{2+1}{4}$ ....(LCM of $2$ and $3$ is $6$; $2$ and $4$ is $4$)

$⟹$ $\frac{x}{6}=\frac{3}{4}$ ...(On simplifying)

$⟹$ $x=\frac{3}{4}\times 6$ ....(Transposing $6$ to RHS)

$⟹$ $x=\frac{9}{2}$.

$\therefore$ $x=\frac{9}{2}$ is the required solution.