1. **State the problem:** Solve the inequality $$w + \frac{1}{2} \geq -\frac{2}{5}$$ for $$w$$. 2. **Formula and rule:** To isolate $$w$$, use the additive property of inequality which states that adding or subtracting the same number on both sides keeps the inequality true. 3. **Subtract $$\frac{1}{2}$$ from both sides:** $$w + \frac{1}{2} - \frac{1}{2} \geq -\frac{2}{5} - \frac{1}{2}$$ 4. **Simplify left side:** $$w \geq -\frac{2}{5} - \frac{1}{2}$$ 5. **Find common denominator for right side:** The denominators are 5 and 2, so common denominator is 10. 6. **Rewrite fractions:** $$-\frac{2}{5} = -\frac{4}{10}, \quad -\frac{1}{2} = -\frac{5}{10}$$ 7. **Add the fractions:** $$-\frac{4}{10} - \frac{5}{10} = -\frac{9}{10}$$ 8. **Final solution:** $$w \geq -\frac{9}{10}$$ This means $$w$$ is greater than or equal to $$-0.9$$.