$$ \begin{aligned} \frac{3}{2}(x+1) &= 3&& \text{simplify left side} \\[1 em]\frac{3x+3}{2} &= 3&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{3x+3}{2} &= 2\cdot3&& \text{cancel out the denominators} \\[1 em]3x+3 &= 6&& \text{ move 3 to the right } \\[1 em]3x &= 6-3&& \\[1 em]3x &= 3&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{3}{3}&& \\[1 em]x &= 1&& \\[1 em] \end{aligned} $$

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