1. **State the problem:** Solve the equation $$2\left(\frac{1}{2}q + 1\right) = -3(2q - 1) + 8q + 4$$ for $q$. 2. **Distribute the constants inside the parentheses:** $$2 \times \frac{1}{2}q + 2 \times 1 = -3 \times 2q + (-3) \times (-1) + 8q + 4$$ which simplifies to $$q + 2 = -6q + 3 + 8q + 4$$ 3. **Combine like terms on the right side:** $$q + 2 = (-6q + 8q) + (3 + 4)$$ $$q + 2 = 2q + 7$$ 4. **Bring all terms involving $q$ to one side and constants to the other:** $$q + 2 = 2q + 7$$ Subtract $2q$ from both sides: $$q - \cancel{2q} + 2 = \cancel{2q} + 7$$ which is $$q - 2q + 2 = 7$$ $$-q + 2 = 7$$ 5. **Subtract 2 from both sides:** $$-q + \cancel{2} = 7 - \cancel{2}$$ $$-q = 5$$ 6. **Multiply both sides by $-1$ to solve for $q$:** $$\cancel{-1} \times (-q) = 5 \times \cancel{-1}$$ $$q = -5$$ **Final answer:** $$q = -5$$