$$\frac{x}{5}-1 = \frac{x}{7}+3$$

$$ \begin{aligned} \frac{x}{5}-1 &= \frac{x}{7}+3&& \text{multiply ALL terms by } \color{blue}{ 35 }. \\[1 em]35 \cdot \frac{x}{5}-35\cdot1 &= 35 \cdot \frac{x}{7}+35\cdot3&& \text{cancel out the denominators} \\[1 em]7x-35 &= 5x+105&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ -35 }$ to the right} \\[1 em]7x-5x &= 105+35&& \text{simplify left and right hand side} \\[1 em]2x &= 140&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{140}{2}&& \\[1 em]x &= 70&& \\[1 em] \end{aligned} $$

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