$$ \begin{aligned} \frac{10-x}{x} &= 1&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x \cdot \frac{10-x}{x} &= x\cdot1&& \text{cancel out the denominators} \\[1 em]10-x &= x&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 10 }$ to the right} \\[1 em]-x-x &= -10&& \text{simplify left side} \\[1 em]-2x &= -10&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-10}{-2}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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