$$ \begin{aligned} x-\frac{1}{6} &= \frac{3}{10}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30x-30\cdot\frac{1}{6} &= 30\cdot\frac{3}{10}&& \text{cancel out the denominators} \\[1 em]30x-5 &= 9&& \text{ move -5 to the right } \\[1 em]30x &= 9+5&& \\[1 em]30x &= 14&& \text{ divide both sides by $ 30 $ } \\[1 em]x &= \frac{14}{30}&& \\[1 em]x &= \frac{7}{15}&& \\[1 em] \end{aligned} $$

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