Inequality Solution 9Cff4C

1. **State the problem:** Solve the inequality $$\frac{z}{9} \geq 4$$ and graph the solutions. 2. **Formula and rules:** To solve inequalities involving fractions, multiply both sides by the denominator to isolate the variable. Since 9 is positive, the inequality direction remains the same. 3. **Step-by-step solution:** $$\frac{z}{9} \geq 4$$ Multiply both sides by 9: $$\cancel{9} \times \frac{z}{\cancel{9}} \geq 4 \times 9$$ Simplifies to: $$z \geq 36$$ 4. **Interpretation:** The solution is all values of $z$ greater than or equal to 36. 5. **Graphing:** On a number line, shade all values from 36 to infinity, including 36 (closed circle). **Final answer:** $$z \geq 36$$