$$ \begin{aligned} \frac{x}{8}+3 &= 5x&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8 \cdot \frac{x}{8}+8\cdot3 &= 8\cdot5x&& \text{cancel out the denominators} \\[1 em]x+24 &= 40x&& \text{move the $ \color{blue}{ 40x } $ to the left side and $ \color{blue}{ 24 }$ to the right} \\[1 em]x-40x &= -24&& \text{simplify left side} \\[1 em]-39x &= -24&& \text{ divide both sides by $ -39 $ } \\[1 em]x &= \frac{-24}{-39}&& \\[1 em]x &= \frac{8}{13}&& \\[1 em] \end{aligned} $$

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