Which option gives the correct solution set of −3 < x ≤ 2 for x ∈ Z?

Correct answer: {−2, −1, 0, 1, 2}

Because x belongs to the integers, list only whole-number values, not every real number in the interval. The inequality −3 < x excludes −3, while x ≤ 2 includes 2. The integers strictly greater than −3 and at most 2 are −2, −1, 0, 1, and 2. Hence the solution set is {−2, −1, 0, 1, 2}, option A. Option B incorrectly includes the excluded endpoint −3. Option C omits the included endpoint 2, and option D includes −3 while omitting 2. A useful check is to test both boundary values separately and then list each consecutive integer between them. Therefore A is the complete and correct integer solution set.