$$ \begin{aligned} \frac{5}{7}x-4 &= \frac{3}{7}x+1&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7 \cdot \frac{5}{7}x-7\cdot4 &= 7 \cdot \frac{3}{7}x+7\cdot1&& \text{cancel out the denominators} \\[1 em]5x-28 &= 3x+7&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -28 }$ to the right} \\[1 em]5x-3x &= 7+28&& \text{simplify left and right hand side} \\[1 em]2x &= 35&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{35}{2}&& \\[1 em] \end{aligned} $$

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