Question

Solve for |4x+3| < 9

Answer 1

Under the absolute value could be positive or negative number, but absolute value make them both positive.
For positive number we can write is (4x+3) and for negative  -(4x+3)
 4x+3<9
4x< 6
x< 3/2    (-∞, 3/2)

 -(4x+3)<9
-4x-12<9
-4x<21
x>-21/4        (-21/4, +∞)

 (-∞, 3/2)∩  (-21/4, +∞) =(-21/4, 3/2) it could be written as (-5.25,  1.5)