$$ \begin{aligned} 3x-\frac{1}{9}\cdot27 &= 18&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9\cdot3x-9 \cdot \frac{1}{9}\cdot27 &= 9\cdot18&& \text{cancel out the denominators} \\[1 em]27x-27 &= 162&& \text{ move -27 to the right } \\[1 em]27x &= 162+27&& \\[1 em]27x &= 189&& \text{ divide both sides by $ 27 $ } \\[1 em]x &= \frac{189}{27}&& \\[1 em]x &= 7&& \\[1 em] \end{aligned} $$

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