$$ \begin{aligned} \frac{x}{2}-x+\frac{3}{5} &= 3&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10 \cdot \frac{x}{2}-10x+10\cdot\frac{3}{5} &= 10\cdot3&& \text{cancel out the denominators} \\[1 em]5x-10x+6 &= 30&& \text{simplify left side} \\[1 em]-5x+6 &= 30&& \text{ move 6 to the right } \\[1 em]-5x &= 30-6&& \\[1 em]-5x &= 24&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= -\frac{24}{5}&& \\[1 em] \end{aligned} $$

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