1. **Problem statement:** Solve the inequality $-7z \geq 14$ in the set of real numbers. 2. **Formula and rules:** To solve inequalities, isolate the variable on one side. Remember, when dividing or multiplying by a negative number, reverse the inequality sign. 3. **Step-by-step solution:** - Start with $-7z \geq 14$. - Divide both sides by $-7$ (note the inequality sign reverses): $$z \leq \frac{14}{-7}$$ - Simplify: $$z \leq -2$$ 4. **Interpretation:** The solution set is all real numbers less than or equal to $-2$, which is the interval $(-\infty, -2]$. **Final answer:** $$\boxed{(-\infty, -2]}$$