$$ \begin{aligned} \frac{13}{2}x+12 &= -24+11x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{13}{2}x+2\cdot12 &= -2\cdot24+2\cdot11x&& \text{cancel out the denominators} \\[1 em]13x+24 &= -48+22x&& \text{move the $ \color{blue}{ 22x } $ to the left side and $ \color{blue}{ 24 }$ to the right} \\[1 em]13x-22x &= -48-24&& \text{simplify left and right hand side} \\[1 em]-9x &= -72&& \text{ divide both sides by $ -9 $ } \\[1 em]x &= \frac{-72}{-9}&& \\[1 em]x &= 8&& \\[1 em] \end{aligned} $$

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