$$ \begin{aligned} \frac{7}{9} &= \frac{x}{x-10}&& \text{multiply ALL terms by } \color{blue}{ 9(x-10) }. \\[1 em]9(x-10)\cdot\frac{7}{9} &= 9(x-10)\frac{x}{x-10}&& \text{cancel out the denominators} \\[1 em]7x-70 &= 9x&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ -70 }$ to the right} \\[1 em]7x-9x &= 70&& \text{simplify left side} \\[1 em]-2x &= 70&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= -\frac{70}{2}&& \\[1 em]x &= -35&& \\[1 em] \end{aligned} $$

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