|x+1|+|x+2|=2

There are two cases to consider:

Case 1: x+1 > 0 and x+2 > 0
In this case, the equation simplifies to:
x+1 + x+2 = 2
2x + 3 = 2
2x = -1
x = -1/2

Case 2: x+1 < 0 and x+2 < 0
In this case, the equation simplifies to:
-(x+1) - (x+2) = 2
-x - 1 - x - 2 = 2
-2x - 3 = 2
-2x = 5
x = -5/2

Therefore, the solutions to the equation |x+1|+|x+2|=2 are x = -1/2 and x = -5/2.