$$\frac{3}{4}(x+4)+x = \frac{1}{2}(x+1)$$

$$ \begin{aligned} \frac{3}{4}(x+4)+x &= \frac{1}{2}(x+1)&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{3}{4}(x+4)+4x &= 4 \cdot \frac{1}{2}(x+1)&& \text{cancel out the denominators} \\[1 em]3x+12+4x &= 2x+2&& \text{simplify left side} \\[1 em]7x+12 &= 2x+2&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]7x-2x &= 2-12&& \text{simplify left and right hand side} \\[1 em]5x &= -10&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{10}{5}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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