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

$$ \begin{aligned} \frac{x}{2}+\frac{x}{3}+\frac{x}{4} &= 13&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{x}{2}+12\frac{x}{3}+12\frac{x}{4} &= 12\cdot13&& \text{cancel out the denominators} \\[1 em]6x+4x+3x &= 156&& \text{simplify left side} \\[1 em]13x &= 156&& \text{ divide both sides by $ 13 $ } \\[1 em]x &= \frac{156}{13}&& \\[1 em]x &= 12&& \\[1 em] \end{aligned} $$

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