$$ \begin{aligned} \frac{5}{7}x+4 &= \frac{2}{2}x-3&& \text{multiply ALL terms by } \color{blue}{ 14 }. \\[1 em]14 \cdot \frac{5}{7}x+14\cdot4 &= 14 \cdot \frac{2}{2}x-14\cdot3&& \text{cancel out the denominators} \\[1 em]10x+56 &= 14x-42&& \text{move the $ \color{blue}{ 14x } $ to the left side and $ \color{blue}{ 56 }$ to the right} \\[1 em]10x-14x &= -42-56&& \text{simplify left and right hand side} \\[1 em]-4x &= -98&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= \frac{-98}{-4}&& \\[1 em]x &= \frac{49}{2}&& \\[1 em] \end{aligned} $$

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