1. **State the problem:** Solve the inequality $$-4(3x + 2) < -3x + 2$$. 2. **Apply the distributive property:** Multiply $$-4$$ by each term inside the parentheses. $$-4 \times 3x = -12x$$ $$-4 \times 2 = -8$$ So the inequality becomes: $$-12x - 8 < -3x + 2$$ 3. **Isolate variable terms on one side:** Add $$12x$$ to both sides to move all $$x$$ terms to the right. $$-12x - 8 + 12x < -3x + 2 + 12x$$ Simplify: $$\cancel{-12x} - 8 + \cancel{12x} < (-3x + 12x) + 2$$ $$-8 < 9x + 2$$ 4. **Isolate the constant term on the other side:** Subtract $$2$$ from both sides. $$-8 - 2 < 9x + 2 - 2$$ Simplify: $$-10 < 9x + \cancel{2} - \cancel{2}$$ $$-10 < 9x$$ 5. **Solve for $$x$$:** Divide both sides by $$9$$. $$\frac{-10}{9} < \frac{9x}{9}$$ Simplify: $$\frac{-10}{9} < x$$ 6. **Rewrite the inequality:** This is equivalent to $$x > \frac{-10}{9}$$ 7. **Interpret the solution:** The solution is all $$x$$ values greater than $$-\frac{10}{9}$$. **Answer choice:** A $$x > -\frac{10}{9}$$