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

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