$$ \begin{aligned} \frac{2}{9}v+7 &= \frac{1}{3}v+5&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9 \cdot \frac{2}{9}v+9\cdot7 &= 9 \cdot \frac{1}{3}v+9\cdot5&& \text{cancel out the denominators} \\[1 em]2v+63 &= 3v+45&& \text{move the $ \color{blue}{ 3v } $ to the left side and $ \color{blue}{ 63 }$ to the right} \\[1 em]2v-3v &= 45-63&& \text{simplify left and right hand side} \\[1 em]-v &= -18&& \text{switch signs on both sides} \\[1 em]v &= 18&& \\[1 em] \end{aligned} $$

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