Question
$\frac{\text{x}}{2}+\frac{\text{x}}{3}+\frac{\text{x}}{4}=13$
✓
Answer
We have:$\frac{\text{x}}{2}+\frac{\text{x}}{3}+\frac{\text{x}}{4}=13$
$L.C.M.$ of $2, 3, 4 = 12$
$\therefore\frac{\text{x}}{2}+\frac{\text{x}}{3}+\frac{\text{x}}{4}=13$
$6\text{x}+4\text{x}+3\text{x}=13\times12$
$\Rightarrow13\text{x}=156$
$\frac{13\text{x}}{13}=\frac{156}{13}$ (Dividing both sides by $13$)
$\Rightarrow\text{x}=12$
$\therefore\text{x}=12$
Verification: $\text{L.H.S}=\frac{\text{x}}{2}+\frac{\text{x}}{3}+\frac{\text{x}}{4}$
$=\frac{12}{2}+\frac{12}{3}+\frac{12}{4}=6+4+3$
$=13=\text{R.H.S}$
$L.C.M.$ of $2, 3, 4 = 12$
$\therefore\frac{\text{x}}{2}+\frac{\text{x}}{3}+\frac{\text{x}}{4}=13$
$6\text{x}+4\text{x}+3\text{x}=13\times12$
$\Rightarrow13\text{x}=156$
$\frac{13\text{x}}{13}=\frac{156}{13}$ (Dividing both sides by $13$)
$\Rightarrow\text{x}=12$
$\therefore\text{x}=12$
Verification: $\text{L.H.S}=\frac{\text{x}}{2}+\frac{\text{x}}{3}+\frac{\text{x}}{4}$
$=\frac{12}{2}+\frac{12}{3}+\frac{12}{4}=6+4+3$
$=13=\text{R.H.S}$
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