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

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

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