$$ \begin{aligned} \frac{1}{9}(x+18)+\frac{1}{3}(x+3) &= x+3&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9 \cdot \frac{1}{9}(x+18)+9\frac{1}{3}(x+3) &= 9x+9\cdot3&& \text{cancel out the denominators} \\[1 em]x+18+3x+9 &= 9x+27&& \text{simplify left side} \\[1 em]4x+27 &= 9x+27&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ 27 }$ to the right} \\[1 em]4x-9x &= 27-27&& \text{simplify left and right hand side} \\[1 em]-5x &= 0&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{0}{-5}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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