$$\frac{1+x}{2}+\frac{3-x}{4} = -14x\cdot3-13x\cdot2+3x-9$$

$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= -14x\cdot3-13x\cdot2+3x-9&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= -414x\cdot3-413x\cdot2+4\cdot3x-4\cdot9&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= -168x-104x+12x-36&& \text{simplify left and right hand side} \\[1 em]x+5 &= -260x-36&& \text{move the $ \color{blue}{ -260x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]x+260x &= -36-5&& \text{simplify left and right hand side} \\[1 em]261x &= -41&& \text{ divide both sides by $ 261 $ } \\[1 em]x &= -\frac{41}{261}&& \\[1 em] \end{aligned} $$

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