x - 2 |3x + 4| = 10

1. Case 1: 3x + 4 >= 0 (x >= -4/3). Then |3x + 4| = 3x + 4. The equation becomes x - 2(3x + 4) = 10, which simplifies to x - 6x - 8 = 10, so -5x = 18, and x = -18/5. This contradicts x >= -4/3, so no solution in this case.
2. Case 2: 3x + 4 < 0 (x < -4/3). Then |3x + 4| = -(3x + 4). The equation becomes x - 2(-(3x + 4)) = 10, which simplifies to x + 6x + 8 = 10, so 7x = 2, and x = 2/7. This contradicts x < -4/3, so no solution in this case.
3. Final Answer: No solution.