Explanation

This question concerns absolute value, which is best thought of as the distance of something from zero. In this question, the distance of from zero is less than . In this question, and in every question with absolute value, there are two possible cases: the distance in question can be either to the left or to the right. For example, if is on the left side of 0, then it's a negative quantity. And if the distance is less than than, in this case, the left-side case,



because it must be right of on the number line and that's what "greater than" means. We can further clarify this case by adding to both sides of the inequality, getting





Meanwhile, answer choices (A) and (B) are negative, but they are both less than , since they are to the left of -1.5 on the number line.

There is another case: the distance from zero could be on the right side, in positive numbers. Then,







There is one answer choice that fits this case: (C). Note that, to evaluate absolute value, we break it into two cases, one positive and one negative, and in those cases the absolute value vertical bar notation is not required. The correct answer is (C).