$$ \begin{aligned} 3 \cdot \frac{x}{5}+\frac{x}{2} &= 5 \cdot \frac{x}{4}-3&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20\cdot3 \cdot \frac{x}{5}+20\frac{x}{2} &= 20\cdot5 \cdot \frac{x}{4}-20\cdot3&& \text{cancel out the denominators} \\[1 em]12x+10x &= 25x-60&& \text{simplify left side} \\[1 em]22x &= 25x-60&& \text{move the $ \color{blue}{ 25x } $ to the left side} \\[1 em]22x-25x &= -60&& \text{simplify left side} \\[1 em]-3x &= -60&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= \frac{-60}{-3}&& \\[1 em]x &= 20&& \\[1 em] \end{aligned} $$

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