$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= 3(x-2)&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= 4\cdot3(x-2)&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= 12x-24&& \text{simplify left side} \\[1 em]x+5 &= 12x-24&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]x-12x &= -24-5&& \text{simplify left and right hand side} \\[1 em]-11x &= -29&& \text{ divide both sides by $ -11 $ } \\[1 em]x &= \frac{-29}{-11}&& \\[1 em]x &= \frac{29}{11}&& \\[1 em] \end{aligned} $$

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