$$ \begin{aligned} x+\frac{1}{10}x &= 6520&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10x+10 \cdot \frac{1}{10}x &= 10\cdot6520&& \text{cancel out the denominators} \\[1 em]10x+x &= 65200&& \text{simplify left side} \\[1 em]11x &= 65200&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{65200}{11}&& \\[1 em] \end{aligned} $$

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