$$ \begin{aligned} 1 \cdot \frac{x}{2}+\frac{1}{4} &= \frac{1}{6}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot1 \cdot \frac{x}{2}+12\cdot\frac{1}{4} &= 12\cdot\frac{1}{6}&& \text{cancel out the denominators} \\[1 em]6x+3 &= 2&& \text{ move 3 to the right } \\[1 em]6x &= 2-3&& \\[1 em]6x &= -1&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{1}{6}&& \\[1 em] \end{aligned} $$

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