$$ \begin{aligned} \frac{2}{5}x+\frac{4}{5}x-4 &= 1&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{2}{5}x+5\frac{4}{5}x-5\cdot4 &= 5\cdot1&& \text{cancel out the denominators} \\[1 em]2x+4x-20 &= 5&& \text{simplify left side} \\[1 em]6x-20 &= 5&& \text{ move -20 to the right } \\[1 em]6x &= 5+20&& \\[1 em]6x &= 25&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{25}{6}&& \\[1 em] \end{aligned} $$

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