$$5x-\frac{1}{5} = 3 \cdot \frac{x}{2}$$

$$ \begin{aligned} 5x-\frac{1}{5} &= 3 \cdot \frac{x}{2}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot5x-10\cdot\frac{1}{5} &= 10\cdot3 \cdot \frac{x}{2}&& \text{cancel out the denominators} \\[1 em]50x-2 &= 15x&& \text{move the $ \color{blue}{ 15x } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]50x-15x &= 2&& \text{simplify left side} \\[1 em]35x &= 2&& \text{ divide both sides by $ 35 $ } \\[1 em]x &= \frac{2}{35}&& \\[1 em] \end{aligned} $$

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