$$ \begin{aligned} \frac{3}{7} &= 3v&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7\cdot\frac{3}{7} &= 7\cdot3v&& \text{cancel out the denominators} \\[1 em]3 &= 21v&& \text{ swap the left and right side of the equation } \\[1 em]21v &= 3&& \text{ divide both sides by $ 21 $ } \\[1 em]v &= \frac{3}{21}&& \\[1 em]v &= \frac{1}{7}&& \\[1 em] \end{aligned} $$

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