$$ \begin{aligned} \frac{3}{2}x-1 &= 2x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{3}{2}x-2\cdot1 &= 2\cdot2x&& \text{cancel out the denominators} \\[1 em]3x-2 &= 4x&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]3x-4x &= 2&& \text{simplify left side} \\[1 em]-x &= 2&& \text{switch signs on both sides} \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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