$$ \begin{aligned} \frac{x}{3}+\frac{x}{7} &= 10&& \text{multiply ALL terms by } \color{blue}{ 21 }. \\[1 em]21 \cdot \frac{x}{3}+21\frac{x}{7} &= 21\cdot10&& \text{cancel out the denominators} \\[1 em]7x+3x &= 210&& \text{simplify left side} \\[1 em]10x &= 210&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{210}{10}&& \\[1 em]x &= 21&& \\[1 em] \end{aligned} $$

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