$$x+\frac{5}{8} = \frac{x}{4}+\frac{1}{4}$$

$$ \begin{aligned} x+\frac{5}{8} &= \frac{x}{4}+\frac{1}{4}&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8x+8\cdot\frac{5}{8} &= 8 \cdot \frac{x}{4}+8\cdot\frac{1}{4}&& \text{cancel out the denominators} \\[1 em]8x+5 &= 2x+2&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]8x-2x &= 2-5&& \text{simplify left and right hand side} \\[1 em]6x &= -3&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{3}{6}&& \\[1 em]x &= -\frac{1}{2}&& \\[1 em] \end{aligned} $$

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