Question

Solve: |2x + 3| -1 < 4

Answer 1

Add 1
  |2x +3| < 5
Unfold
  -5 < 2x +3 < 5
Subtract 3
  -8 < 2x < 2
Divide by 2
  -4 < x < 1

The solution is
  -4 < x < 1

_____
If you subtract 4 from both sides, you get an expression that compares to zero. Most graphing calculators will show you the zero-crossings, so you can easily find the values of x where this is true.

Answer 2

|2x+3|-1<4
|2x+3|<5

1) when 2x +3 is positive     
2x+3<5
2x<2
x<1    (-∞, 1)

2) when 2x+3 is negative
-(2x+3)<5
-2x-3<5
-2x<8
x>-4  (-4, ∞)

(-∞, 1)∩(-4, ∞)=(-4,1)