$$ \begin{aligned} \frac{41}{4}x+680 &= \frac{25}{5}x+410&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20 \cdot \frac{41}{4}x+20\cdot680 &= 20 \cdot \frac{25}{5}x+20\cdot410&& \text{cancel out the denominators} \\[1 em]205x+13600 &= 100x+8200&& \text{move the $ \color{blue}{ 100x } $ to the left side and $ \color{blue}{ 13600 }$ to the right} \\[1 em]205x-100x &= 8200-13600&& \text{simplify left and right hand side} \\[1 em]105x &= -5400&& \text{ divide both sides by $ 105 $ } \\[1 em]x &= -\frac{5400}{105}&& \\[1 em]x &= -\frac{360}{7}&& \\[1 em] \end{aligned} $$

This page was created using