To solve the equation |x+3| + |x-2| = 7, we will consider the cases when x has different values.

Case 1: x ≥ 2
In this case, both x + 3 and x - 2 are positive, so the equation becomes:
x + 3 + x - 2 = 7
2x + 1 = 7
2x = 6
x = 3

Case 2: -3 ≤ x < 2
In this case, x + 3 is positive and x - 2 is negative, so the equation becomes:
x + 3 - (x - 2) = 7
x + 3 - x + 2 = 7
5 = 7
This case has no solution.

Case 3: x < -3
In this case, both x + 3 and x - 2 are negative, so the equation becomes:
-(x + 3) - (x - 2) = 7
-x - 3 - x + 2 = 7

Therefore, the solutions to the equation |x+3| + |x-2| = 7 are x = 3 and x = -4.