The solution set for 1<|x+3|<4 is:
x ∈ (-2, 2)
To solve this inequality, we first need to isolate the absolute value. This gives us:
|x+3| - 1 < 4 - 1
We can then remove the absolute value signs by considering two cases:
* Case 1: x + 3 > 0
In this case, we have:
x + 3 < 5
Solving for x, we get:
x < 2
* Case 2: x + 3 < 0
In this case, we have:
-(x + 3) < 5
Multiplying both sides by -1, we get:
x + 3 > -5
Solving for x, we get:
x > -8
Combining the solutions from both cases, we get:
x ∈ (-2, 2)