1. **State the problem:** Solve the inequality $-\frac{z}{2} + 4 \geq 2$ for $z$. 2. **Isolate the variable term:** Subtract 4 from both sides to get $$ -\frac{z}{2} \geq 2 - 4 $$ which simplifies to $$ -\frac{z}{2} \geq -2 $$ 3. **Multiply both sides by -2:** Since we multiply by a negative number, the inequality direction flips: $$ z \leq (-2) \times (-2) $$ which simplifies to $$ z \leq 4 $$ 4. **Conclusion:** The solution set is all $z$ such that $$ z \leq 4 $$