$$ \begin{aligned} 8x-\frac{5}{2} &= \frac{5}{5}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot8x-10\cdot\frac{5}{2} &= 10\cdot\frac{5}{5}&& \text{cancel out the denominators} \\[1 em]80x-25 &= 10&& \text{ move -25 to the right } \\[1 em]80x &= 10+25&& \\[1 em]80x &= 35&& \text{ divide both sides by $ 80 $ } \\[1 em]x &= \frac{35}{80}&& \\[1 em]x &= \frac{7}{16}&& \\[1 em] \end{aligned} $$

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