$$ \begin{aligned} \frac{n}{2}-2\frac{n}{3}+4\frac{n}{5} &= 1&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{n}{2}-30\cdot2\frac{n}{3}+30\cdot4\frac{n}{5} &= 30\cdot1&& \text{cancel out the denominators} \\[1 em]15n-20n+24n &= 30&& \text{simplify left side} \\[1 em]19n &= 30&& \text{ divide both sides by $ 19 $ } \\[1 em]n &= \frac{30}{19}&& \\[1 em] \end{aligned} $$

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