$$ \begin{aligned} \frac{9x-11}{2} &= \frac{19x+11}{3}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{9x-11}{2} &= 6 \cdot \frac{19x+11}{3}&& \text{cancel out the denominators} \\[1 em]27x-33 &= 38x+22&& \text{move the $ \color{blue}{ 38x } $ to the left side and $ \color{blue}{ -33 }$ to the right} \\[1 em]27x-38x &= 22+33&& \text{simplify left and right hand side} \\[1 em]-11x &= 55&& \text{ divide both sides by $ -11 $ } \\[1 em]x &= -\frac{55}{11}&& \\[1 em]x &= -5&& \\[1 em] \end{aligned} $$

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