$$ \begin{aligned} \frac{31}{5}+n &= 9&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot\frac{31}{5}+5n &= 5\cdot9&& \text{cancel out the denominators} \\[1 em]31+5n &= 45&& \text{ move 31 to the right } \\[1 em]5n &= 45-31&& \\[1 em]5n &= 14&& \text{ divide both sides by $ 5 $ } \\[1 em]n &= \frac{14}{5}&& \\[1 em] \end{aligned} $$

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