$$ \begin{aligned} \frac{2}{3}x+1+\frac{4}{9}x &= 5&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9 \cdot \frac{2}{3}x+9\cdot1+9\frac{4}{9}x &= 9\cdot5&& \text{cancel out the denominators} \\[1 em]6x+9+4x &= 45&& \text{simplify left side} \\[1 em]10x+9 &= 45&& \text{ move 9 to the right } \\[1 em]10x &= 45-9&& \\[1 em]10x &= 36&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{36}{10}&& \\[1 em]x &= \frac{18}{5}&& \\[1 em] \end{aligned} $$

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