$$\frac{v}{2}-3 = 5+\frac{v}{2}$$

$$ \begin{aligned} \frac{v}{2}-3 &= 5+\frac{v}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{v}{2}-2\cdot3 &= 2\cdot5+2 \cdot \frac{v}{2}&& \text{cancel out the denominators} \\[1 em]v-6 &= 10+v&& \text{move the $ \color{blue}{ v } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]v-v &= 10+6&& \text{simplify left and right hand side} \\[1 em]v-v &= 16&& \\[1 em]0 &= 16&& \\[1 em] \end{aligned} $$

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