Question 5

x ≥ 9

To solve the inequality -4/3 x + 4 ≥ 16, we first isolate x by subtracting 4 from both sides, leading to -4/3 x ≥ 12. Multiplying both sides by -3/4 (which reverses the inequality) results in x ≥ 9.

A) x ≥ 9

This option correctly represents the solution to the inequality. By isolating x, we determine that x must be greater than or equal to 9 to satisfy the original inequality.

B) x ≤ 9

This option is incorrect as it suggests that x can be less than or equal to 9. However, the solution shows that x must be greater than or equal to 9, not less.

C) x = 9

This choice inaccurately implies that x can only equal 9. While 9 is a solution to the inequality, the correct solution is that x can be any value greater than or equal to 9.

D) x < 9

This option is incorrect because it contradicts the solution derived from the inequality. The inequality allows for values of x that are greater than or equal to 9, not less than 9.

Conclusion

The correct answer is definitively x ≥ 9, as it accurately reflects the range of values that satisfy the original inequality. All other options fail to capture the complete solution, either restricting x incorrectly or misrepresenting the relationship derived from the inequality.