$$ \begin{aligned} x-\frac{9}{5}x &= 32&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5x-5 \cdot \frac{9}{5}x &= 5\cdot32&& \text{cancel out the denominators} \\[1 em]5x-9x &= 160&& \text{simplify left side} \\[1 em]-4x &= 160&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= -\frac{160}{4}&& \\[1 em]x &= -40&& \\[1 em] \end{aligned} $$

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