$$ \begin{aligned} \frac{3}{2}q+4-\frac{1}{3}q &= -\frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{3}{2}q+6\cdot4-6\frac{1}{3}q &= -6\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]9q+24-2q &= -5&& \text{simplify left side} \\[1 em]7q+24 &= -5&& \text{ move 24 to the right } \\[1 em]7q &= -5-24&& \\[1 em]7q &= -29&& \text{ divide both sides by $ 7 $ } \\[1 em]q &= -\frac{29}{7}&& \\[1 em] \end{aligned} $$

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