Question

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

Answer 1

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

Making the denominators same in LHS and RHS,

$\Rightarrow \frac{2x+3}{2}\times \frac{3}{3}+\frac{4x-5}{6}=\frac{x}{3}\times \frac{2}{2}$

$\Rightarrow \frac{6x+9}{6}+\frac{4x-5}{6}=\frac{2x}{6}$

$\Rightarrow \frac{6x+9+4x-5}{6}=\frac{2x}{6}$

$\Rightarrow \frac{10x+4}{6}=\frac{2x}{6}$

$\Rightarrow 10x+4=2x$

$\Rightarrow 10x-2x=-4$

$\Rightarrow 8x=-4$

$\Rightarrow x=\frac{-4}{8}=-\frac{1}{2}$

$\therefore x=-\frac{1}{2}$