Final answer:
Upon solving the inequality, it is realized that the given inequality simplifies to an untrue statement, indicating that there is no solution for K. None of the provided options A through D are correct.
Step-by-step explanation:
To solve the inequality 24 + 6K < -6(-4 - K), we first distribute the -6 on the right-hand side:
As we can see, the terms on both sides are the same, which simplifies to 0 < 0, which is not a true statement. Therefore, there is no solution for the inequality, and none of the given options A, B, C, or D are correct.
If this were a different problem and we were supposed to find the solution, we would begin by expanding the right-hand side, moving all terms involving K to one side, and then isolating K by dividing both sides by the coefficient of K.