$$ \begin{aligned} 2x+\frac{3}{3}-3\frac{x}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot2x+6\cdot\frac{3}{3}-6\cdot3\frac{x}{2} &= 6\cdot0&& \text{cancel out the denominators} \\[1 em]12x+6-9x &= 0&& \text{simplify left side} \\[1 em]3x+6 &= 0&& \text{ move the constants to the right } \\[1 em]3x &= -6&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{6}{3}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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