$$ \begin{aligned} \frac{x}{21}+\frac{x}{24} &= 10&& \text{multiply ALL terms by } \color{blue}{ 168 }. \\[1 em]168 \cdot \frac{x}{21}+168\frac{x}{24} &= 168\cdot10&& \text{cancel out the denominators} \\[1 em]8x+7x &= 1680&& \text{simplify left side} \\[1 em]15x &= 1680&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= \frac{1680}{15}&& \\[1 em]x &= 112&& \\[1 em] \end{aligned} $$

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