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

$$ \begin{aligned} \frac{x-2}{3} &= \frac{x+1}{4}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{x-2}{3} &= 12 \cdot \frac{x+1}{4}&& \text{cancel out the denominators} \\[1 em]4x-8 &= 3x+3&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -8 }$ to the right} \\[1 em]4x-3x &= 3+8&& \text{simplify left and right hand side} \\[1 em]x &= 11&& \\[1 em]x &= 11&& \\[1 em] \end{aligned} $$

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