$$\frac{x+4}{x} = \frac{3}{7}$$

$$ \begin{aligned} \frac{x+4}{x} &= \frac{3}{7}&& \text{multiply ALL terms by } \color{blue}{ x\cdot7 }. \\[1 em]x\cdot7 \cdot \frac{x+4}{x} &= x\cdot7\cdot\frac{3}{7}&& \text{cancel out the denominators} \\[1 em]7x+28 &= 3x&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 28 }$ to the right} \\[1 em]7x-3x &= -28&& \text{simplify left side} \\[1 em]4x &= -28&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{28}{4}&& \\[1 em]x &= -7&& \\[1 em] \end{aligned} $$

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