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

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