Question 17

x ≤ -40

To solve the inequality (1/8)x ≤ (1/2)x + 15, we can first rearrange it to isolate x. After simplifying, we find that x is less than or equal to -40.

A) x ≤ -24

This option suggests that x can be less than or equal to -24. However, upon solving the inequality, we determined that the correct limit for x is actually -40, making this option incorrect.

B) x ≥ -40

This option indicates that x can be greater than or equal to -40. However, our solution shows that x must be less than or equal to -40, thus rendering this option incorrect.

C) x ≤ -40

This option accurately reflects the solution to the inequality. The process of solving the inequality leads us to conclude that x must indeed be less than or equal to -40, making this the correct choice.

D) x ≥ -24

This choice states that x can be greater than or equal to -24. Since our solution shows that x must be less than or equal to -40, this option does not satisfy the conditions of the inequality and is therefore incorrect.

Conclusion

The correct answer is x ≤ -40, as derived from the steps taken to solve the inequality. All other options either propose a range that does not include values less than or equal to -40 or suggest incorrect limits for x based on the given inequality.