$$ \begin{aligned} \frac{x}{2}-\frac{1}{4} &= 3 \cdot \frac{x}{4}+1&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{x}{2}-4\cdot\frac{1}{4} &= 4\cdot3 \cdot \frac{x}{4}+4\cdot1&& \text{cancel out the denominators} \\[1 em]2x-1 &= 3x+4&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -1 }$ to the right} \\[1 em]2x-3x &= 4+1&& \text{simplify left and right hand side} \\[1 em]-x &= 5&& \text{switch signs on both sides} \\[1 em]x &= -5&& \\[1 em] \end{aligned} $$

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