$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= -\frac{5}{4}x-5&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= -4 \cdot \frac{5}{4}x-4\cdot5&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= -5x-20&& \text{simplify left side} \\[1 em]x+5 &= -5x-20&& \text{move the $ \color{blue}{ -5x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]x+5x &= -20-5&& \text{simplify left and right hand side} \\[1 em]6x &= -25&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{25}{6}&& \\[1 em] \end{aligned} $$

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