I understand the way to solve this problem, but I'm still not sure as to why d. is correct and not a. Is is because d is a more "complete" range of correct values?
The question asks you for the range of values for which the inequality holds. So basically, you need to give all values of x for which the inequality holds. Since -1/3 < x< 0 is also a part of this solution, (D) includes all value. (A) is only a part of this solution.
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