$$ \begin{aligned} \frac{4}{9} &= \frac{1}{15}x\cdot3&& \text{multiply ALL terms by } \color{blue}{ 45 }. \\[1 em]45\cdot\frac{4}{9} &= 45 \cdot \frac{1}{15}x\cdot3&& \text{cancel out the denominators} \\[1 em]20 &= 9x&& \text{ swap the left and right side of the equation } \\[1 em]9x &= 20&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{20}{9}&& \\[1 em] \end{aligned} $$

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