$$ \begin{aligned} -\frac{1}{6}x-\frac{3}{4} &= 0&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]-12 \cdot \frac{1}{6}x-12\cdot\frac{3}{4} &= 12\cdot0&& \text{cancel out the denominators} \\[1 em]-2x-9 &= 0&& \text{ move the constants to the right } \\[1 em]-2x &= 9&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= -\frac{9}{2}&& \\[1 em] \end{aligned} $$

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