$$ \begin{aligned} -\frac{5}{8}x+2+\frac{3}{4}x-1 &= 0&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]-8 \cdot \frac{5}{8}x+8\cdot2+8\frac{3}{4}x-8\cdot1 &= 8\cdot0&& \text{cancel out the denominators} \\[1 em]-5x+16+6x-8 &= 0&& \text{simplify left side} \\[1 em]x+8 &= 0&& \text{ move the constants to the right } \\[1 em]x &= -8&& \\[1 em]x &= -8&& \\[1 em] \end{aligned} $$

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