SOLUTION: |x+2|<2x+7

1.  If x+2 >= 0, then  |x+2| = x+2.

    Hence, in the domain x >= -2 the inequality (1) takes the form

    x + 2 < 2x + 7,   or  2-7 < x,  which is  x > -5.

    In other words, in the domain x >= -2 the solution set is x > -5.
    Thus for the domain x > -2 the solution set is the intersection [,)  and  (,), i.e.  [,).


2.  If x+2 < 0, then  |x+2| = -(x+2).

    Hence, in the domain x < -2 the inequality (1) takes the form

    -(x + 2) < 2x + 7,   or  -x - 2 < 2x +7,  or  -2-7 < 3x,  or  -9 < 3x, which is  x > -3.

    In other words, in the domain x < -2 the solution set is x > -3.
    Thus for the domain x < -2 the solution set is the intersection (,)  and  (,), i.e.  (,).


3.  Finally, combining these two cases, we obtain the solution set as  (,) U [,,  i.e.  (,).