$$ \begin{aligned} -9+\frac{x}{13}+10 &= 8&& \text{multiply ALL terms by } \color{blue}{ 13 }. \\[1 em]-13\cdot9+13 \cdot \frac{x}{13}+13\cdot10 &= 13\cdot8&& \text{cancel out the denominators} \\[1 em]-117+x+130 &= 104&& \text{simplify left side} \\[1 em]x+13 &= 104&& \text{ move 13 to the right } \\[1 em]x &= 104-13&& \\[1 em]x &= 91&& \\[1 em]x &= 91&& \\[1 em] \end{aligned} $$

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