$$ \begin{aligned} 5x+\frac{3}{4} &= \frac{1}{8}&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8\cdot5x+8\cdot\frac{3}{4} &= 8\cdot\frac{1}{8}&& \text{cancel out the denominators} \\[1 em]40x+6 &= 1&& \text{ move 6 to the right } \\[1 em]40x &= 1-6&& \\[1 em]40x &= -5&& \text{ divide both sides by $ 40 $ } \\[1 em]x &= -\frac{5}{40}&& \\[1 em]x &= -\frac{1}{8}&& \\[1 em] \end{aligned} $$

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