$$ \begin{aligned} 9x+\frac{3}{8} &= \frac{3}{8}x+9&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8\cdot9x+8\cdot\frac{3}{8} &= 8 \cdot \frac{3}{8}x+8\cdot9&& \text{cancel out the denominators} \\[1 em]72x+3 &= 3x+72&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]72x-3x &= 72-3&& \text{simplify left and right hand side} \\[1 em]69x &= 69&& \text{ divide both sides by $ 69 $ } \\[1 em]x &= \frac{69}{69}&& \\[1 em]x &= 1&& \\[1 em] \end{aligned} $$

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