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

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