$$ \begin{aligned} 3+\frac{x}{7} &= 2 \cdot \frac{x}{5}&& \text{multiply ALL terms by } \color{blue}{ 35 }. \\[1 em]35\cdot3+35 \cdot \frac{x}{7} &= 35\cdot2 \cdot \frac{x}{5}&& \text{cancel out the denominators} \\[1 em]105+5x &= 14x&& \text{move the $ \color{blue}{ 14x } $ to the left side and $ \color{blue}{ 105 }$ to the right} \\[1 em]5x-14x &= -105&& \text{simplify left side} \\[1 em]-9x &= -105&& \text{ divide both sides by $ -9 $ } \\[1 em]x &= \frac{-105}{-9}&& \\[1 em]x &= \frac{35}{3}&& \\[1 em] \end{aligned} $$

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