x - 2 |3x + 2| = 16

1. Case 1: 3x + 2 >= 0 (x >= -2/3). Then |3x + 2| = 3x + 2. The equation becomes x - 2(3x + 2) = 16, which simplifies to x - 6x - 4 = 16, so -5x = 20, and x = -4. This contradicts x >= -2/3, so no solution in this case.
2. Case 2: 3x + 2 < 0 (x < -2/3). Then |3x + 2| = -(3x + 2). The equation becomes x - 2(-(3x + 2)) = 16, which simplifies to x + 6x + 4 = 16, so 7x = 12, and x = 12/7. This contradicts x < -2/3, so no solution in this case.
3. Final Answer: No solution.