$$ \begin{aligned} \frac{x}{5}+\frac{x}{7} &= 12&& \text{multiply ALL terms by } \color{blue}{ 35 }. \\[1 em]35 \cdot \frac{x}{5}+35\frac{x}{7} &= 35\cdot12&& \text{cancel out the denominators} \\[1 em]7x+5x &= 420&& \text{simplify left side} \\[1 em]12x &= 420&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= \frac{420}{12}&& \\[1 em]x &= 35&& \\[1 em] \end{aligned} $$

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