1. **State the problem:** Solve the inequality $$3(8 - 4x) < 6(x - 5)$$ and determine which number line represents the solution set. 2. **Apply the distributive property:** $$3 \times 8 - 3 \times 4x < 6 \times x - 6 \times 5$$ which simplifies to $$24 - 12x < 6x - 30$$ 3. **Move all terms involving $x$ to one side and constants to the other:** Add $12x$ to both sides: $$24 - \cancel{12x} + 12x < 6x + 12x - 30$$ which simplifies to $$24 < 18x - 30$$ Add $30$ to both sides: $$24 + 30 < 18x - 30 + 30$$ $$54 < 18x$$ 4. **Isolate $x$ by dividing both sides by 18:** $$\frac{54}{\cancel{18}} < \frac{18x}{\cancel{18}}$$ which simplifies to $$3 < x$$ 5. **Rewrite the inequality:** $$x > 3$$ 6. **Interpret the solution:** The solution set is all $x$ values greater than 3. 7. **Match with the number line:** The number line with an open circle at 3 and shading to the right represents $x > 3$. **Final answer:** The center number line with an open circle at 3 and shading to the right represents the solution set.