$$ \begin{aligned} \frac{5}{9}x+32 &= x&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9 \cdot \frac{5}{9}x+9\cdot32 &= 9x&& \text{cancel out the denominators} \\[1 em]5x+288 &= 9x&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ 288 }$ to the right} \\[1 em]5x-9x &= -288&& \text{simplify left side} \\[1 em]-4x &= -288&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= \frac{-288}{-4}&& \\[1 em]x &= 72&& \\[1 em] \end{aligned} $$

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