$$ \begin{aligned} -\frac{2}{x} &= 4&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]-x\cdot\frac{2}{x} &= x\cdot4&& \text{cancel out the denominators} \\[1 em]-2 &= 4x&& \text{ swap the left and right side of the equation } \\[1 em]4x &= -2&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{2}{4}&& \\[1 em]x &= -\frac{1}{2}&& \\[1 em] \end{aligned} $$

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