$$ \begin{aligned} x+\frac{5}{8} &= 2x-\frac{5}{8}&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8x+8\cdot\frac{5}{8} &= 8\cdot2x-8\cdot\frac{5}{8}&& \text{cancel out the denominators} \\[1 em]8x+5 &= 16x-5&& \text{move the $ \color{blue}{ 16x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]8x-16x &= -5-5&& \text{simplify left and right hand side} \\[1 em]-8x &= -10&& \text{ divide both sides by $ -8 $ } \\[1 em]x &= \frac{-10}{-8}&& \\[1 em]x &= \frac{5}{4}&& \\[1 em] \end{aligned} $$

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