$$ \begin{aligned} 7 \cdot \frac{x}{8}-3\frac{x}{5} &= \frac{11}{2}&& \text{multiply ALL terms by } \color{blue}{ 40 }. \\[1 em]40\cdot7 \cdot \frac{x}{8}-40\cdot3\frac{x}{5} &= 40\cdot\frac{11}{2}&& \text{cancel out the denominators} \\[1 em]35x-24x &= 220&& \text{simplify left side} \\[1 em]11x &= 220&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{220}{11}&& \\[1 em]x &= 20&& \\[1 em] \end{aligned} $$

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