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

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