$$7-\frac{8}{x} = 9$$

$$ \begin{aligned} 7-\frac{8}{x} &= 9&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot7-x\cdot\frac{8}{x} &= x\cdot9&& \text{cancel out the denominators} \\[1 em]7x-8 &= 9x&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ -8 }$ to the right} \\[1 em]7x-9x &= 8&& \text{simplify left side} \\[1 em]-2x &= 8&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= -\frac{8}{2}&& \\[1 em]x &= -4&& \\[1 em] \end{aligned} $$

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