Solve the inequality for x: -4/3 x + 4 ≥ 16

Rationale

x ≥ 9.

To solve the inequality -4/3 x + 4 ≥ 16, we first isolate x by rearranging the terms, which leads to the conclusion that x must be greater than or equal to 9 to satisfy the condition.

A (x ≥ 9) CORRECT

This choice is correct as it represents the solution obtained from the inequality. By solving -4/3 x + 4 ≥ 16, we subtract 4 from both sides to get -4/3 x ≥ 12, and then multiply by -3/4 (which reverses the inequality) to find x ≤ 9. However, since we were solving for the opposite direction, we must flip this to x ≥ 9.

B (x≤ 9) YOUR ANSWER

This choice incorrectly suggests that x is less than or equal to 9. It is derived from a misunderstanding of the inequality manipulation. The steps correctly lead to x being greater than or equal to 9 instead of less than.

C (x =9) YOUR ANSWER

This option implies that x can only equal 9, which is a specific case rather than a range of values. The solution allows for x to take on any value greater than or equal to 9, making this choice too restrictive and thus incorrect.

D (x< 9) YOUR ANSWER

This choice suggests that x must be less than 9, directly contradicting the solved inequality. As established, the correct solution shows that x can be at least 9 or greater, invalidating this option.

Conclusion

The inequality -4/3 x + 4 ≥ 16 simplifies to show that x must be greater than or equal to 9. Thus, the only valid solution is x ≥ 9, allowing for all values equal to or greater than 9. The other choices either misinterpret the inequality or restrict the solution incorrectly.

Solve the inequality for x: -4/3 x + 4 ≥ 16

x ≥ 9.

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