1. **State the problem:** Solve the inequality $4x \geq -9$ for $x$. 2. **Recall the rule for inequalities:** When dividing or multiplying both sides of an inequality by a positive number, the inequality direction remains the same. 3. **Divide both sides by 4:** $$4x \geq -9$$ Divide both sides by 4: $$\frac{\cancel{4}x}{\cancel{4}} \geq \frac{-9}{4}$$ 4. **Simplify:** $$x \geq -\frac{9}{4}$$ 5. **Interpretation:** The solution is all values of $x$ greater than or equal to $-\frac{9}{4}$. **Final answer:** $$x \geq -\frac{9}{4}$$