$$ \begin{aligned} \frac{x-65}{x}\cdot100 &= 35&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x \cdot \frac{x-65}{x}\cdot100 &= x\cdot35&& \text{cancel out the denominators} \\[1 em]100x-6500 &= 35x&& \text{move the $ \color{blue}{ 35x } $ to the left side and $ \color{blue}{ -6500 }$ to the right} \\[1 em]100x-35x &= 6500&& \text{simplify left side} \\[1 em]65x &= 6500&& \text{ divide both sides by $ 65 $ } \\[1 em]x &= \frac{6500}{65}&& \\[1 em]x &= 100&& \\[1 em] \end{aligned} $$

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