We can solve the inequality |x + 3| < 1 by considering two cases:
Case 1: x + 3 ≥ 0
If x + 3 ≥ 0, then the inequality simplifies to:
x + 3 < 1
Subtracting 3 from both sides gives:
x < -2
So the solution set for this case is -3 < x < -2.
Case 2: x + 3 < 0
If x + 3 < 0, then we have:
-(x + 3) < 1
Multiplying both sides by -1 (which reverses the direction of the inequality) gives:
x + 3 > -1
Subtracting 3 from both sides gives:
x > -4
So the solution set for this case is -4 < x < -3.
Combining the solution sets from both cases, we get:
-4 < x < -2
Therefore, the solution to the inequality |x + 3| < 1 is the open interval (-4, -2).