$$ \begin{aligned} \frac{x}{3} &= \frac{3}{4}-\frac{x}{2}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{x}{3} &= 12\cdot\frac{3}{4}-12\frac{x}{2}&& \text{cancel out the denominators} \\[1 em]4x &= 9-6x&& \text{move the $ \color{blue}{ -6x } $ to the left side} \\[1 em]4x+6x &= 9&& \text{simplify left side} \\[1 em]10x &= 9&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{9}{10}&& \\[1 em] \end{aligned} $$

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