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

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