$$ \begin{aligned} \frac{2}{3}x-\frac{1}{3}x+11 &= 8&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{2}{3}x-3\frac{1}{3}x+3\cdot11 &= 3\cdot8&& \text{cancel out the denominators} \\[1 em]2x-x+33 &= 24&& \text{simplify left side} \\[1 em]x+33 &= 24&& \text{ move 33 to the right } \\[1 em]x &= 24-33&& \\[1 em]x &= -9&& \\[1 em]x &= -9&& \\[1 em] \end{aligned} $$

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