$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= 2x\cdot2-16x+35&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= 42x\cdot2-4\cdot16x+4\cdot35&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= 16x-64x+140&& \text{simplify left and right hand side} \\[1 em]x+5 &= -48x+140&& \text{move the $ \color{blue}{ -48x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]x+48x &= 140-5&& \text{simplify left and right hand side} \\[1 em]49x &= 135&& \text{ divide both sides by $ 49 $ } \\[1 em]x &= \frac{135}{49}&& \\[1 em] \end{aligned} $$

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