To solve the equation |x+1| + |x-2| = 3, we need to consider the different cases for the absolute values.

Case 1: x+1 ≥ 0 and x-2 ≥ 0
In this case, both absolute values are positive, so we can remove the absolute value signs. The equation becomes x+1 + x-2 = 3.
Combining like terms, we get 2x - 1 = 3.
Adding 1 to both sides, we have 2x = 4.
Dividing both sides by 2, we find x = 2.

Case 2: x+1 ≥ 0 and x-2 < 0
In this case, the absolute value of (x-2) is negative, so we need to change the sign. The equation becomes x+1 - (x-2) = 3.
Simplifying, we get x + 1 - x + 2 = 3.
Combining like terms, we have 3 = 3.
This equation is always true, so any value of x that satisfies x+1 ≥ 0 will work. Therefore, x can be any number greater than or equal to -1.

Case 3: x+1 < 0 and x-2 ≥ 0
In this case, the absolute value of (x+1) is negative, so we need to change the sign. The equation becomes -(x+1) + (x-2) = 3.
Simplifying, we get -x - 1 + x - 2 = 3.
Combining like terms, we have -3 = 3.
This equation is never true, so there are no solutions in this case.

Case 4: x+1 < 0 and x-2 < 0
In this case, both absolute values are negative, so we can remove the absolute value signs. The equation becomes -(x+1) - (x-2) = 3.
Simplifying, we get -x - 1 - x + 2 = 3.
Combining like terms, we have -2x + 1 = 3.
Subtracting 1 from both sides, we get -2x = 2.
Dividing both sides by -2, we find x = -1.

Therefore, the solutions to the equation |x+1| + |x-2| = 3 are x = 2 and x = -1.