$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= \frac{1}{2}x-14&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= 4 \cdot \frac{1}{2}x-4\cdot14&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= 2x-56&& \text{simplify left side} \\[1 em]x+5 &= 2x-56&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]x-2x &= -56-5&& \text{simplify left and right hand side} \\[1 em]-x &= -61&& \text{switch signs on both sides} \\[1 em]x &= 61&& \\[1 em] \end{aligned} $$

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