1. **State the problem:** Solve the inequality $$3 \leq 1 + 6 \left(-4x - \frac{5}{3}\right)$$. 2. **Distribute the 6:** Multiply 6 by each term inside the parentheses: $$3 \leq 1 + 6 \times (-4x) + 6 \times \left(-\frac{5}{3}\right)$$ $$3 \leq 1 - 24x - 10$$ 3. **Simplify the right side:** $$3 \leq 1 - 10 - 24x$$ $$3 \leq -9 - 24x$$ 4. **Isolate the variable term:** Subtract -9 from both sides: $$3 + 9 \leq -9 - 24x + 9$$ $$12 \leq -24x$$ 5. **Divide both sides by -24:** Remember, dividing by a negative number reverses the inequality sign: $$\frac{12}{\cancel{-24}} \geq \frac{-24x}{\cancel{-24}}$$ $$-\frac{1}{2} \geq x$$ 6. **Rewrite the solution:** $$x \leq -\frac{1}{2}$$ **Final answer:** $$x \leq -\frac{1}{2}$$