$$ \begin{aligned} \frac{2}{x}-3 &= 7&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{2}{x}-x\cdot3 &= x\cdot7&& \text{cancel out the denominators} \\[1 em]2-3x &= 7x&& \text{move the $ \color{blue}{ 7x } $ to the left side and $ \color{blue}{ 2 }$ to the right} \\[1 em]-3x-7x &= -2&& \text{simplify left side} \\[1 em]-10x &= -2&& \text{ divide both sides by $ -10 $ } \\[1 em]x &= \frac{-2}{-10}&& \\[1 em]x &= \frac{1}{5}&& \\[1 em] \end{aligned} $$

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