Final answer:
The solution to the inequality |x + 6| > 6 requires examining two cases due to the absolute value, resulting in the solution set: x > 0 or x < -12. Always remember to check the answer to ensure it is reasonable.
Step-by-step explanation:
The inequality given appears to be "|x + 6| > 6". To solve this algebraically, we consider two cases due to the absolute value:
- x + 6 > 6, which simplifies to x > 0 after subtracting 6 from both sides.
- x + 6 < -6, which simplifies to x < -12 after subtracting 6 from both sides.
The solution to the inequality is all x values greater than 0 and less than -12. Therefore, the solution set is: x > 0 or x < -12.
It's also important to check the answer to see if it is reasonable, which in this case, the answer does comply with the original inequality stating that the absolute value is greater than 6.