$$10x\cdot2-\frac{10}{5} = 0$$

$$ \begin{aligned} 10x\cdot2-\frac{10}{5} &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]510x\cdot2-5\cdot\frac{10}{5} &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]100x-10 &= 0&& \text{ move the constants to the right } \\[1 em]100x &= 10&& \text{ divide both sides by $ 100 $ } \\[1 em]x &= \frac{10}{100}&& \\[1 em]x &= \frac{1}{10}&& \\[1 em] \end{aligned} $$

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