$$ \begin{aligned} \frac{9}{11} &= \frac{x}{19}&& \text{multiply ALL terms by } \color{blue}{ 209 }. \\[1 em]209\cdot\frac{9}{11} &= 209 \cdot \frac{x}{19}&& \text{cancel out the denominators} \\[1 em]171 &= 11x&& \text{ swap the left and right side of the equation } \\[1 em]11x &= 171&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{171}{11}&& \\[1 em] \end{aligned} $$

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