$$\frac{1}{x+8} = 10$$

$$ \begin{aligned} \frac{1}{x+8} &= 10&& \text{multiply ALL terms by } \color{blue}{ x+8 }. \\[1 em](x+8)\cdot\frac{1}{x+8} &= (x+8)\cdot10&& \text{cancel out the denominators} \\[1 em]1 &= 10x+80&& \text{ swap the left and right side of the equation } \\[1 em]10x+80 &= 1&& \text{ move 80 to the right } \\[1 em]10x &= 1-80&& \\[1 em]10x &= -79&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= -\frac{79}{10}&& \\[1 em] \end{aligned} $$

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