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

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