$$ \begin{aligned} 7 \cdot \frac{x}{8}-3\frac{x}{8} &= 1&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8\cdot7 \cdot \frac{x}{8}-8\cdot3\frac{x}{8} &= 8\cdot1&& \text{cancel out the denominators} \\[1 em]7x-3x &= 8&& \text{simplify left side} \\[1 em]4x &= 8&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{8}{4}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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