$$ \begin{aligned} 7n-\frac{1}{2} &= \frac{20}{9}&& \text{multiply ALL terms by } \color{blue}{ 18 }. \\[1 em]18\cdot7n-18\cdot\frac{1}{2} &= 18\cdot\frac{20}{9}&& \text{cancel out the denominators} \\[1 em]126n-9 &= 40&& \text{ move -9 to the right } \\[1 em]126n &= 40+9&& \\[1 em]126n &= 49&& \text{ divide both sides by $ 126 $ } \\[1 em]n &= \frac{49}{126}&& \\[1 em]n &= \frac{7}{18}&& \\[1 em] \end{aligned} $$

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