$$ \begin{aligned} \frac{a}{5} &= \frac{a-10}{7}&& \text{multiply ALL terms by } \color{blue}{ 35 }. \\[1 em]35 \cdot \frac{a}{5} &= 35 \cdot \frac{a-10}{7}&& \text{cancel out the denominators} \\[1 em]7a &= 5a-50&& \text{move the $ \color{blue}{ 5a } $ to the left side} \\[1 em]7a-5a &= -50&& \text{simplify left side} \\[1 em]2a &= -50&& \text{ divide both sides by $ 2 $ } \\[1 em]a &= -\frac{50}{2}&& \\[1 em]a &= -25&& \\[1 em] \end{aligned} $$

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