To solve the inequality -2 < x + 2 ≤ 5, we need to isolate x in the middle of the two inequalities.
Starting with x + 2 ≤ 5, we can subtract 2 from both sides to get:
x ≤ 3
Next, for -2 < x + 2, we can subtract 2 from both sides to get:
-4 < x
So the complete solution is:
-4 < x ≤ 3
This means that the correct answer is option (C): x > -4 and x ≤ 3.