$$ \begin{aligned} x &= \frac{1000}{10}\cdot1&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10x &= 10 \cdot \frac{1000}{10}\cdot1&& \text{cancel out the denominators} \\[1 em]10x &= 1000&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{1000}{10}&& \\[1 em]x &= 100&& \\[1 em] \end{aligned} $$
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