$$ \begin{aligned} \frac{5}{3}x &= 32-x&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{5}{3}x &= 3\cdot32-3x&& \text{cancel out the denominators} \\[1 em]5x &= 96-3x&& \text{move the $ \color{blue}{ -3x } $ to the left side} \\[1 em]5x+3x &= 96&& \text{simplify left side} \\[1 em]8x &= 96&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= \frac{96}{8}&& \\[1 em]x &= 12&& \\[1 em] \end{aligned} $$

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