Start by dividing all terms by 4, to reduce this expression: |x+1| < 3.
Case 1: x+1 is already positive. The abs. val. operator does not change
anything. Then x+1<3, or x<2.
Case 2: (x+1) is negative. The abs. val. operator, in effect, puts a - sign in
front of (x+1): -(x+1)<3. Distributing the - sign: -x - 1 < 3. Adding 1 to both sides: -x < 4. We want to solve for positive x, so we mult. both sides of
-x<4 by -1 AND change the direction of the inequality symbol:
x > -4
Thus, the solution set is (-4,2): All real numbers between -4 and 2.