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

$$ \begin{aligned} \frac{x+1}{3} &= \frac{1}{2}x+4&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{x+1}{3} &= 6 \cdot \frac{1}{2}x+6\cdot4&& \text{cancel out the denominators} \\[1 em]2x+2 &= 3x+24&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 2 }$ to the right} \\[1 em]2x-3x &= 24-2&& \text{simplify left and right hand side} \\[1 em]-x &= 22&& \text{switch signs on both sides} \\[1 em]x &= -22&& \\[1 em] \end{aligned} $$

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