$$ \begin{aligned} x-\frac{1}{2} &= \frac{x}{4}+3&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4x-4\cdot\frac{1}{2} &= 4 \cdot \frac{x}{4}+4\cdot3&& \text{cancel out the denominators} \\[1 em]4x-2 &= x+12&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]4x-x &= 12+2&& \text{simplify left and right hand side} \\[1 em]3x &= 14&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{14}{3}&& \\[1 em] \end{aligned} $$

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