1. **State the problem:** Solve the inequality $-4 + 2x \geq 1$. 2. **Add 4 to both sides:** $$-4 + 2x + 4 \geq 1 + 4$$ $$\cancel{-4} + 2x + \cancel{4} \geq 5$$ $$2x \geq 5$$ 3. **Divide both sides by 2:** $$\frac{2x}{2} \geq \frac{5}{2}$$ $$\cancel{2}x \geq \frac{5}{2}$$ $$x \geq \frac{5}{2}$$ 4. **Interpret the solution:** The solution to the inequality is all $x$ values greater than or equal to $\frac{5}{2}$ (which is 2.5). 5. **Check the options:** - I. $-4$ is less than $2.5$, so it does not satisfy the inequality. - II. $-6$ is less than $2.5$, so it does not satisfy the inequality. - III. $3$ is greater than $2.5$, so it satisfies the inequality. **Final answer:** $x \geq \frac{5}{2}$ or $x \geq 2.5$. Only option III satisfies the inequality.