$$ \begin{aligned} \frac{x+3}{10} &= \frac{x}{7}&& \text{multiply ALL terms by } \color{blue}{ 70 }. \\[1 em]70 \cdot \frac{x+3}{10} &= 70 \cdot \frac{x}{7}&& \text{cancel out the denominators} \\[1 em]7x+21 &= 10x&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ 21 }$ to the right} \\[1 em]7x-10x &= -21&& \text{simplify left side} \\[1 em]-3x &= -21&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= \frac{-21}{-3}&& \\[1 em]x &= 7&& \\[1 em] \end{aligned} $$

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