$$ \begin{aligned} \frac{6}{x}+8 &= 11&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{6}{x}+x\cdot8 &= x\cdot11&& \text{cancel out the denominators} \\[1 em]6+8x &= 11x&& \text{move the $ \color{blue}{ 11x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]8x-11x &= -6&& \text{simplify left side} \\[1 em]-3x &= -6&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= \frac{-6}{-3}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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