$$\frac{1+x}{2}+\frac{3-x}{4} = 0$$

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

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