$$\frac{1}{3}x = x-2$$

$$ \begin{aligned} \frac{1}{3}x &= x-2&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{1}{3}x &= 3x-3\cdot2&& \text{cancel out the denominators} \\[1 em]x &= 3x-6&& \text{move the $ \color{blue}{ 3x } $ to the left side} \\[1 em]x-3x &= -6&& \text{simplify left side} \\[1 em]-2x &= -6&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-6}{-2}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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