$$-\frac{6}{x} = -2$$

$$ \begin{aligned} -\frac{6}{x} &= -2&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]-x\cdot\frac{6}{x} &= x\cdot(-2)&& \text{cancel out the denominators} \\[1 em]-6 &= -2x&& \text{ swap the left and right side of the equation } \\[1 em]-2x &= -6&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-6}{-2}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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