$$ \begin{aligned} \frac{3}{2}x+8 &= \frac{1}{4}x-6&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{3}{2}x+4\cdot8 &= 4 \cdot \frac{1}{4}x-4\cdot6&& \text{cancel out the denominators} \\[1 em]6x+32 &= x-24&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 32 }$ to the right} \\[1 em]6x-x &= -24-32&& \text{simplify left and right hand side} \\[1 em]5x &= -56&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{56}{5}&& \\[1 em] \end{aligned} $$

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