Final answer:
To solve the inequality |x+7|-x > 12, consider two cases: x > 2 and x < -2. There is no solution for x > 2, but for x < -2, the solution is x < -9.5.
Step-by-step explanation:
To solve the inequality |x+7|-x > 12, we need to consider two cases: x > 2 and x < -2.
Case 1:
If x > 2, then |x+7| = x+7. So, the inequality becomes (x+7)-x > 12, which simplifies to 7 > 12, which is false. Therefore, there is no solution for x > 2.
Case 2:
If x < -2, then |x+7| = -(x+7). So, the inequality becomes -(x+7)-x > 12, which simplifies to -x-7-x > 12, which further simplifies to -2x - 7 > 12.
Adding 7 to both sides, we get -2x > 19. Dividing both sides by -2 (remember to reverse the inequality when dividing by a negative number), we get x < -9.5.
Therefore, the solution to the inequality |x+7|-x > 12 is x < -9.5.