$$\frac{7}{9} = \frac{b}{b}-10$$

$$ \begin{aligned} \frac{7}{9} &= \frac{b}{b}-10&& \text{multiply ALL terms by } \color{blue}{ 9b }. \\[1 em]9b\cdot\frac{7}{9} &= 9b\frac{b}{b}-9b\cdot10&& \text{cancel out the denominators} \\[1 em]7b &= 9b-90b&& \text{simplify right side} \\[1 em]7b &= -81b&& \text{move the $ \color{blue}{ -81b } $ to the left side} \\[1 em]7b+81b &= 0&& \text{simplify left side} \\[1 em]88b &= 0&& \text{ divide both sides by $ 88 $ } \\[1 em]b &= \frac{0}{88}&& \\[1 em]b &= 0&& \\[1 em] \end{aligned} $$

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