$$ \begin{aligned} \frac{x}{3}-5\frac{x}{6} &= \frac{1}{3}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{x}{3}-6\cdot5\frac{x}{6} &= 6\cdot\frac{1}{3}&& \text{cancel out the denominators} \\[1 em]2x-5x &= 2&& \text{simplify left side} \\[1 em]-3x &= 2&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= -\frac{2}{3}&& \\[1 em] \end{aligned} $$

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