$$ \begin{aligned} 2x-\frac{1}{3} &= 2-x&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot2x-3\cdot\frac{1}{3} &= 3\cdot2-3x&& \text{cancel out the denominators} \\[1 em]6x-1 &= 6-3x&& \text{move the $ \color{blue}{ -3x } $ to the left side and $ \color{blue}{ -1 }$ to the right} \\[1 em]6x+3x &= 6+1&& \text{simplify left and right hand side} \\[1 em]9x &= 7&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{7}{9}&& \\[1 em] \end{aligned} $$

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