$$ \begin{aligned} 8 \cdot \frac{x}{9}-2x &= 0&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9\cdot8 \cdot \frac{x}{9}-9\cdot2x &= 9\cdot0&& \text{cancel out the denominators} \\[1 em]8x-18x &= 0&& \text{simplify left side} \\[1 em]-10x &= 0&& \text{ divide both sides by $ -10 $ } \\[1 em]x &= \frac{0}{-10}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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