$$ \begin{aligned} 2-\frac{1}{3}x &= \frac{1}{6}x+1&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot2-6 \cdot \frac{1}{3}x &= 6 \cdot \frac{1}{6}x+6\cdot1&& \text{cancel out the denominators} \\[1 em]12-2x &= x+6&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]-2x-x &= 6-12&& \text{simplify left and right hand side} \\[1 em]-3x &= -6&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= \frac{-6}{-3}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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