$$\frac{5x+5}{8} = \frac{2x-1}{2}$$

$$ \begin{aligned} \frac{5x+5}{8} &= \frac{2x-1}{2}&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8 \cdot \frac{5x+5}{8} &= 8 \cdot \frac{2x-1}{2}&& \text{cancel out the denominators} \\[1 em]5x+5 &= 8x-4&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]5x-8x &= -4-5&& \text{simplify left and right hand side} \\[1 em]-3x &= -9&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= \frac{-9}{-3}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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