$$ \begin{aligned} \frac{1}{4}x-\frac{1}{2}x+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{4}x-4\frac{1}{2}x+4\cdot1 &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]x-2x+4 &= 0&& \text{simplify left side} \\[1 em]-x+4 &= 0&& \text{ move the constants to the right } \\[1 em]-x &= -4&& \text{switch signs on both sides} \\[1 em]x &= 4&& \\[1 em] \end{aligned} $$

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