Solve the inequality for x: (1/8)x ? (1/2)x + 15

Rationale

x ≤ -40

To solve the inequality \((1/8)x ≤ (1/2)x + 15\), we first isolate \(x\) by moving all \(x\) terms to one side and constants to the other, which leads us to find that \(x\) must be less than or equal to -40.

A (x ≤-24) YOUR ANSWER

This choice suggests that \(x\) is less than or equal to -24, which does not satisfy the derived inequality. When substituting values like -24 back into the original inequality, it fails to hold true, indicating that -24 is not a valid solution.

B (x ≥ -40) YOUR ANSWER

While this choice appears to be correct, it is actually repeated in option C. It indicates that \(x\) can be less than or equal to -40, but it is not the only option presented. Therefore, it does not uniquely identify the solution.

C (x ≤ -40) CORRECT

This choice accurately reflects the solution derived from the inequality. Upon solving, we find that when \(x\) is less than or equal to -40, the original inequality holds true, making this the correct answer.

D (x ≥ -24) YOUR ANSWER

Similar to option A, this choice fails to satisfy the inequality derived from the problem. Values such as -24 do not fulfill the condition established by the inequality, thus making it an incorrect option.

Conclusion

The inequality \((1/8)x ≤ (1/2)x + 15\) simplifies to \(x ≤ -40\). Thus, the correct answer is C, indicating that values of \(x\) less than or equal to -40 satisfy the original inequality. Options A and D misrepresent the solution, while option B, although correct, is redundant as it is the same as C.

Solve the inequality for x: (1/8)x ? (1/2)x + 15

x ≤ -40

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