$$\frac{x-2}{3}+\frac{x+1}{6} = \frac{3}{2}$$

$$ \begin{aligned} \frac{x-2}{3}+\frac{x+1}{6} &= \frac{3}{2}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{x-2}{3}+6\frac{x+1}{6} &= 6\cdot\frac{3}{2}&& \text{cancel out the denominators} \\[1 em]2x-4+x+1 &= 9&& \text{simplify left side} \\[1 em]3x-3 &= 9&& \text{ move -3 to the right } \\[1 em]3x &= 9+3&& \\[1 em]3x &= 12&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{12}{3}&& \\[1 em]x &= 4&& \\[1 em] \end{aligned} $$

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