$$ \begin{aligned} -\frac{x}{4} &= \frac{x}{7}+9&& \text{multiply ALL terms by } \color{blue}{ 28 }. \\[1 em]-28 \cdot \frac{x}{4} &= 28 \cdot \frac{x}{7}+28\cdot9&& \text{cancel out the denominators} \\[1 em]-7x &= 4x+252&& \text{move the $ \color{blue}{ 4x } $ to the left side} \\[1 em]-7x-4x &= 252&& \text{simplify left side} \\[1 em]-11x &= 252&& \text{ divide both sides by $ -11 $ } \\[1 em]x &= -\frac{252}{11}&& \\[1 em] \end{aligned} $$

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