$$2 \cdot \frac{x}{3}+\frac{1}{2} = \frac{x}{2}-\frac{3}{4}$$

$$ \begin{aligned} 2 \cdot \frac{x}{3}+\frac{1}{2} &= \frac{x}{2}-\frac{3}{4}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot2 \cdot \frac{x}{3}+12\cdot\frac{1}{2} &= 12 \cdot \frac{x}{2}-12\cdot\frac{3}{4}&& \text{cancel out the denominators} \\[1 em]8x+6 &= 6x-9&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]8x-6x &= -9-6&& \text{simplify left and right hand side} \\[1 em]2x &= -15&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{15}{2}&& \\[1 em] \end{aligned} $$

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