$$ \begin{aligned} 11 \cdot \frac{x}{6} &= 0&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot11 \cdot \frac{x}{6} &= 6\cdot0&& \text{cancel out the denominators} \\[1 em]11x &= 0&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{0}{11}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$
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