$$ \begin{aligned} \frac{1}{2}v+\frac{2}{5}v-\frac{3}{4}v &= 6&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20 \cdot \frac{1}{2}v+20\frac{2}{5}v-20\frac{3}{4}v &= 20\cdot6&& \text{cancel out the denominators} \\[1 em]10v+8v-15v &= 120&& \text{simplify left side} \\[1 em]3v &= 120&& \text{ divide both sides by $ 3 $ } \\[1 em]v &= \frac{120}{3}&& \\[1 em]v &= 40&& \\[1 em] \end{aligned} $$

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