Question

Solve each of the following equations and also verify your solution :

$\frac{x}{2}+\frac{x}{3}+\frac{x}{4}=13$

Answer 1

We have $\frac{x}{2}+\frac{x}{3}+\frac{x}{4}=13$
L.C.M of 2,3,4 = 12
$\therefore \frac{x}{2}+\frac{x}{3}+\frac{x}{4}=136x+4x+3x=13\times 12\Rightarrow 13x=156\frac{13x}{13}=\frac{156}{13}$ (Dividing both sides by 13)
$\Rightarrow x=12\therefore x=12$
Verification :
$L.H.S.=\frac{x}{2}+\frac{x}{3}+\frac{x}{4}=\frac{12}{2}+\frac{12}{3}+\frac{12}{4}=6+4+3=13=R.H.S.$