$$\frac{5}{4}x+2 = \frac{1}{4}+\frac{1}{4}x$$

$$ \begin{aligned} \frac{5}{4}x+2 &= \frac{1}{4}+\frac{1}{4}x&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{5}{4}x+4\cdot2 &= 4\cdot\frac{1}{4}+4\frac{1}{4}x&& \text{cancel out the denominators} \\[1 em]5x+8 &= 1+x&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 8 }$ to the right} \\[1 em]5x-x &= 1-8&& \text{simplify left and right hand side} \\[1 em]4x &= -7&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{7}{4}&& \\[1 em] \end{aligned} $$

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