$$ \begin{aligned} \frac{1}{x} &= \frac{2}{10}&& \text{multiply ALL terms by } \color{blue}{ x\cdot10 }. \\[1 em]x\cdot10\cdot\frac{1}{x} &= x\cdot10\cdot\frac{2}{10}&& \text{cancel out the denominators} \\[1 em]10 &= 2x&& \text{ swap the left and right side of the equation } \\[1 em]2x &= 10&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{10}{2}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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