$$ \begin{aligned} \frac{21}{2}y+6 &= \frac{41}{2}y-1&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{21}{2}y+2\cdot6 &= 2 \cdot \frac{41}{2}y-2\cdot1&& \text{cancel out the denominators} \\[1 em]21y+12 &= 41y-2&& \text{move the $ \color{blue}{ 41y } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]21y-41y &= -2-12&& \text{simplify left and right hand side} \\[1 em]-20y &= -14&& \text{ divide both sides by $ -20 $ } \\[1 em]y &= \frac{-14}{-20}&& \\[1 em]y &= \frac{7}{10}&& \\[1 em] \end{aligned} $$

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