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

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