$$ \begin{aligned} \frac{1}{5}x-9 &= 2x&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{1}{5}x-5\cdot9 &= 5\cdot2x&& \text{cancel out the denominators} \\[1 em]x-45 &= 10x&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ -45 }$ to the right} \\[1 em]x-10x &= 45&& \text{simplify left side} \\[1 em]-9x &= 45&& \text{ divide both sides by $ -9 $ } \\[1 em]x &= -\frac{45}{9}&& \\[1 em]x &= -5&& \\[1 em] \end{aligned} $$

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