$$ \begin{aligned} x+\frac{1}{2}-3\frac{x}{5}+2 &= 1&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10x+10\cdot\frac{1}{2}-10\cdot3\frac{x}{5}+10\cdot2 &= 10\cdot1&& \text{cancel out the denominators} \\[1 em]10x+5-6x+20 &= 10&& \text{simplify left side} \\[1 em]4x+25 &= 10&& \text{ move 25 to the right } \\[1 em]4x &= 10-25&& \\[1 em]4x &= -15&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{15}{4}&& \\[1 em] \end{aligned} $$

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