1. Solve the inequality $10q - 12 < 48 + 5q$. 2. Start by isolating $q$ on one side. 3. Subtract $5q$ from both sides: $$10q - 12 - 5q < 48 + 5q - 5q$$ $$\cancel{10q} - 12 - \cancel{5q} < 48 + \cancel{5q} - \cancel{5q}$$ $$5q - 12 < 48$$ 4. Add 12 to both sides: $$5q - 12 + 12 < 48 + 12$$ $$5q + \cancel{-12} + \cancel{12} < 60$$ $$5q < 60$$ 5. Divide both sides by 5: $$\frac{5q}{\cancel{5}} < \frac{60}{\cancel{5}}$$ $$q < 12$$ 6. The solution is all $q$ such that $q < 12$. This means any number less than 12 satisfies the inequality. Final answer: $$q < 12$$