$$ \begin{aligned} x+\frac{1}{10}x &= 4510&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10x+10 \cdot \frac{1}{10}x &= 10\cdot4510&& \text{cancel out the denominators} \\[1 em]10x+x &= 45100&& \text{simplify left side} \\[1 em]11x &= 45100&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{45100}{11}&& \\[1 em]x &= 4100&& \\[1 em] \end{aligned} $$

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