$$ \begin{aligned} x+\frac{3}{5} &= \frac{3}{5}+\frac{1}{2}x&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10x+10\cdot\frac{3}{5} &= 10\cdot\frac{3}{5}+10\frac{1}{2}x&& \text{cancel out the denominators} \\[1 em]10x+6 &= 6+5x&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]10x-5x &= 6-6&& \text{simplify left and right hand side} \\[1 em]5x &= 0&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{0}{5}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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