$$\frac{x}{3}-3 = \frac{x}{9}+3$$

$$ \begin{aligned} \frac{x}{3}-3 &= \frac{x}{9}+3&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9 \cdot \frac{x}{3}-9\cdot3 &= 9 \cdot \frac{x}{9}+9\cdot3&& \text{cancel out the denominators} \\[1 em]3x-27 &= x+27&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -27 }$ to the right} \\[1 em]3x-x &= 27+27&& \text{simplify left and right hand side} \\[1 em]2x &= 54&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{54}{2}&& \\[1 em]x &= 27&& \\[1 em] \end{aligned} $$

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