$$ \begin{aligned} \frac{1}{5}-\frac{4}{9}x &= \frac{2}{15}&& \text{multiply ALL terms by } \color{blue}{ 45 }. \\[1 em]45\cdot\frac{1}{5}-45\frac{4}{9}x &= 45\cdot\frac{2}{15}&& \text{cancel out the denominators} \\[1 em]9-20x &= 6&& \text{ move 9 to the right } \\[1 em]-20x &= 6-9&& \\[1 em]-20x &= -3&& \text{ divide both sides by $ -20 $ } \\[1 em]x &= \frac{-3}{-20}&& \\[1 em]x &= \frac{3}{20}&& \\[1 em] \end{aligned} $$

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