$$47 = -\frac{x}{11}+43$$

$$ \begin{aligned} 47 &= -\frac{x}{11}+43&& \text{multiply ALL terms by } \color{blue}{ 11 }. \\[1 em]11\cdot47 &= -11 \cdot \frac{x}{11}+11\cdot43&& \text{cancel out the denominators} \\[1 em]517 &= -x+473&& \text{ swap the left and right side of the equation } \\[1 em]-x+473 &= 517&& \text{ move 473 to the right } \\[1 em]-x &= 517-473&& \\[1 em]-x &= 44&& \text{switch signs on both sides} \\[1 em]x &= -44&& \\[1 em] \end{aligned} $$

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