$$ \begin{aligned} 1 &= \frac{3}{2}(3x+4)&& \text{simplify right side} \\[1 em]1 &= \frac{9x+12}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot1 &= 2 \cdot \frac{9x+12}{2}&& \text{cancel out the denominators} \\[1 em]2 &= 9x+12&& \text{ swap the left and right side of the equation } \\[1 em]9x+12 &= 2&& \text{ move 12 to the right } \\[1 em]9x &= 2-12&& \\[1 em]9x &= -10&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= -\frac{10}{9}&& \\[1 em] \end{aligned} $$

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