$$ \begin{aligned} 20-\frac{x}{3} &= \frac{x}{2}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot20-6 \cdot \frac{x}{3} &= 6 \cdot \frac{x}{2}&& \text{cancel out the denominators} \\[1 em]120-2x &= 3x&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 120 }$ to the right} \\[1 em]-2x-3x &= -120&& \text{simplify left side} \\[1 em]-5x &= -120&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{-120}{-5}&& \\[1 em]x &= 24&& \\[1 em] \end{aligned} $$

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