$$47 = -\frac{x}{11}$$

$$ \begin{aligned} 47 &= -\frac{x}{11}&& \text{multiply ALL terms by } \color{blue}{ 11 }. \\[1 em]11\cdot47 &= -11 \cdot \frac{x}{11}&& \text{cancel out the denominators} \\[1 em]517 &= -x&& \text{ swap the left and right side of the equation } \\[1 em]-x &= 517&& \text{switch signs on both sides} \\[1 em]x &= -517&& \\[1 em] \end{aligned} $$

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