$$ \begin{aligned} \frac{2}{5}x &= \frac{2}{9}(x+2)+4&& \text{multiply ALL terms by } \color{blue}{ 45 }. \\[1 em]45 \cdot \frac{2}{5}x &= 45 \cdot \frac{2}{9}(x+2)+45\cdot4&& \text{cancel out the denominators} \\[1 em]18x &= 10x+20+180&& \text{simplify right side} \\[1 em]18x &= 10x+200&& \text{move the $ \color{blue}{ 10x } $ to the left side} \\[1 em]18x-10x &= 200&& \text{simplify left side} \\[1 em]8x &= 200&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= \frac{200}{8}&& \\[1 em]x &= 25&& \\[1 em] \end{aligned} $$

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