$$ \begin{aligned} 5 \cdot \frac{x}{6}-\frac{x}{2} &= 1&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot5 \cdot \frac{x}{6}-6\frac{x}{2} &= 6\cdot1&& \text{cancel out the denominators} \\[1 em]5x-3x &= 6&& \text{simplify left side} \\[1 em]2x &= 6&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{6}{2}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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