$$ \begin{aligned} 3 \cdot \frac{x}{5}-x &= \frac{x}{10}-\frac{5}{2}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot3 \cdot \frac{x}{5}-10x &= 10 \cdot \frac{x}{10}-10\cdot\frac{5}{2}&& \text{cancel out the denominators} \\[1 em]6x-10x &= x-25&& \text{simplify left side} \\[1 em]-4x &= x-25&& \text{move the $ \color{blue}{ x } $ to the left side} \\[1 em]-4x-x &= -25&& \text{simplify left side} \\[1 em]-5x &= -25&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{-25}{-5}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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