$$ \begin{aligned} \frac{2}{5}x+\frac{2}{5} &= \frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{2}{5}x+30\cdot\frac{2}{5} &= 30\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]12x+12 &= 25&& \text{ move 12 to the right } \\[1 em]12x &= 25-12&& \\[1 em]12x &= 13&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= \frac{13}{12}&& \\[1 em] \end{aligned} $$

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