$$ \begin{aligned} \frac{9}{5}x &= 0-\frac{11}{5}&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{9}{5}x &= 5\cdot0-5\cdot\frac{11}{5}&& \text{cancel out the denominators} \\[1 em]9x &= 0-11&& \text{simplify right side} \\[1 em]9x &= -11&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= -\frac{11}{9}&& \\[1 em] \end{aligned} $$

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