$$ \begin{aligned} 6x+27 &= \frac{17}{2}x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot6x+2\cdot27 &= 2 \cdot \frac{17}{2}x&& \text{cancel out the denominators} \\[1 em]12x+54 &= 17x&& \text{move the $ \color{blue}{ 17x } $ to the left side and $ \color{blue}{ 54 }$ to the right} \\[1 em]12x-17x &= -54&& \text{simplify left side} \\[1 em]-5x &= -54&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{-54}{-5}&& \\[1 em]x &= \frac{54}{5}&& \\[1 em] \end{aligned} $$

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