Question

Simplify: $\frac{2x+3}{2}+\frac{4x-5}{6}=\frac{x}{3}$.

Answer 1

Given, $\frac{2x+3}{2}+\frac{4x-5}{6}=\frac{x}{3}$.

$\Rightarrow \frac{3(2x+3)+(4x-5)}{6}=\frac{x}{3}$ …[Cross-multiplying the denominators on the LHS]

$\Rightarrow \frac{6x+9+4x-5}{6}=\frac{x}{3}$ ...[By Distribution Law]

$\Rightarrow \frac{10x+4}{2}=\frac{x}{1}$ ...[Multiplying $3$ on both sides and simplifying]

$\Rightarrow 10x+4=2x$ ...[Multiplying $2$ on both sides]

$\Rightarrow 10x-2x=-4$ ...[Transposing $x$ terms to one side]

$\Rightarrow 8x=-4$

$\Rightarrow x=\frac{-4}{8}$ ...[Dividing $8$ on both sides]

$\Rightarrow$ $x=\frac{-1}{2}$.