$$ \begin{aligned} \frac{5}{2}x-\frac{3}{8}x-2x+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8 \cdot \frac{5}{2}x-8\frac{3}{8}x-8\cdot2x+8\cdot1 &= 8\cdot0&& \text{cancel out the denominators} \\[1 em]20x-3x-16x+8 &= 0&& \text{simplify left side} \\[1 em]x+8 &= 0&& \text{ move the constants to the right } \\[1 em]x &= -8&& \\[1 em]x &= -8&& \\[1 em] \end{aligned} $$

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