$$ \begin{aligned} x+\frac{1}{2} &= \frac{3}{4}x&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4x+4\cdot\frac{1}{2} &= 4 \cdot \frac{3}{4}x&& \text{cancel out the denominators} \\[1 em]4x+2 &= 3x&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 2 }$ to the right} \\[1 em]4x-3x &= -2&& \text{simplify left side} \\[1 em]x &= -2&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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