$$ \begin{aligned} -\frac{1}{3}n+1 &= -7&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]-3 \cdot \frac{1}{3}n+3\cdot1 &= 3\cdot(-7)&& \text{cancel out the denominators} \\[1 em]-n+3 &= -21&& \text{ move 3 to the right } \\[1 em]-n &= -21-3&& \\[1 em]-n &= -24&& \text{switch signs on both sides} \\[1 em]n &= 24&& \\[1 em] \end{aligned} $$

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