$$ \begin{aligned} x+\frac{x}{8} &= 27&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8x+8 \cdot \frac{x}{8} &= 8\cdot27&& \text{cancel out the denominators} \\[1 em]8x+x &= 216&& \text{simplify left side} \\[1 em]9x &= 216&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{216}{9}&& \\[1 em]x &= 24&& \\[1 em] \end{aligned} $$

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