$$ \begin{aligned} \frac{41}{4}x+680 &= \frac{25}{2}x+410&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{41}{4}x+4\cdot680 &= 4 \cdot \frac{25}{2}x+4\cdot410&& \text{cancel out the denominators} \\[1 em]41x+2720 &= 50x+1640&& \text{move the $ \color{blue}{ 50x } $ to the left side and $ \color{blue}{ 2720 }$ to the right} \\[1 em]41x-50x &= 1640-2720&& \text{simplify left and right hand side} \\[1 em]-9x &= -1080&& \text{ divide both sides by $ -9 $ } \\[1 em]x &= \frac{-1080}{-9}&& \\[1 em]x &= 120&& \\[1 em] \end{aligned} $$

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