$$ \begin{aligned} \frac{3}{4}-x &= 2(x+1)&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot\frac{3}{4}-4x &= 4\cdot2(x+1)&& \text{cancel out the denominators} \\[1 em]3-4x &= 8x+8&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]-4x-8x &= 8-3&& \text{simplify left and right hand side} \\[1 em]-12x &= 5&& \text{ divide both sides by $ -12 $ } \\[1 em]x &= -\frac{5}{12}&& \\[1 em] \end{aligned} $$

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