$$ \begin{aligned} \frac{5}{2}x+3 &= 3-(4x+12)&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{5}{2}x+2\cdot3 &= 2\cdot3-2(4x+12)&& \text{cancel out the denominators} \\[1 em]5x+6 &= 6-(8x+24)&& \text{simplify right side} \\[1 em]5x+6 &= 6-8x-24&& \\[1 em]5x+6 &= -8x-18&& \text{move the $ \color{blue}{ -8x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]5x+8x &= -18-6&& \text{simplify left and right hand side} \\[1 em]13x &= -24&& \text{ divide both sides by $ 13 $ } \\[1 em]x &= -\frac{24}{13}&& \\[1 em] \end{aligned} $$

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