1. **State the problem:** Solve the inequality $$4x \geq -9$$ and graph the solution. 2. **Formula and rules:** To solve inequalities, we isolate the variable by performing inverse operations. When dividing or multiplying by a positive number, the inequality direction stays the same. 3. **Solve the inequality:** $$4x \geq -9$$ Divide both sides by 4: $$\frac{\cancel{4}x}{\cancel{4}} \geq \frac{-9}{4}$$ which simplifies to $$x \geq -\frac{9}{4}$$ 4. **Interpretation:** The solution is all values of $$x$$ greater than or equal to $$-\frac{9}{4}$$. 5. **Graphing:** On a number line, draw a solid circle at $$-\frac{9}{4}$$ (because of the $\geq$ sign) and shade the line to the right to represent all $$x$$ values greater than or equal to $$-\frac{9}{4}$$. **Final answer:** $$x \geq -\frac{9}{4}$$