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
2x - 1 = 7 -2x = 8 x = -4
Therefore, the solutions to the equation |x+3| + |x-2| = 7 are x = 3 and x = -4.
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
2x - 1 = 7In this case, both x + 3 and x - 2 are negative, so the equation becomes:
-(x + 3) - (x - 2) = 7
-x - 3 - x + 2 = 7
-2x = 8
x = -4
Therefore, the solutions to the equation |x+3| + |x-2| = 7 are x = 3 and x = -4.