$$ \begin{aligned} n+\frac{31}{2} &= 12&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2n+2\cdot\frac{31}{2} &= 2\cdot12&& \text{cancel out the denominators} \\[1 em]2n+31 &= 24&& \text{ move 31 to the right } \\[1 em]2n &= 24-31&& \\[1 em]2n &= -7&& \text{ divide both sides by $ 2 $ } \\[1 em]n &= -\frac{7}{2}&& \\[1 em] \end{aligned} $$

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