1. **State the problem:** We have two inequalities and sets of possible solutions. We need to determine which numbers satisfy each inequality. 2. **First inequality:** $$x + 212 \geq -52$$ 3. **Solve the first inequality:** Subtract 212 from both sides: $$x + 212 - 212 \geq -52 - 212$$ $$x \geq -264$$ 4. **Check each candidate for the first inequality:** - 0: $0 \geq -264$ is true. - -266: $-266 \geq -264$ is false. - -267: $-267 \geq -264$ is false. - 15: $15 \geq -264$ is true. - 300: $300 \geq -264$ is true. **Correct solutions for first inequality:** 0, 15, 300 5. **Second inequality:** $$\frac{x}{3} < -53$$ 6. **Solve the second inequality:** Multiply both sides by 3 (positive number, inequality direction stays the same): $$\cancel{3} \times \frac{x}{\cancel{3}} < -53 \times 3$$ $$x < -159$$ 7. **Check each candidate for the second inequality:** - 0: $0 < -159$ is false. - -159: $-159 < -159$ is false (not less than). - -200: $-200 < -159$ is true. - -160: $-160 < -159$ is true. - 1.3: $1.3 < -159$ is false. - -158: $-158 < -159$ is false. **Correct solutions for second inequality:** -200, -160 8. **Write the two numbers together to form the code:** From first inequality: 0, 15, 300 From second inequality: -200, -160 Code: **015300-200-160** (or simply list the correct solution numbers as requested: 1,4,5 for first; 3,4 for second)