To solve the inequality \( x + 6 > -2 \), we can start by isolating \( x \).
- Subtract 6 from both sides: \[ x + 6 - 6 > -2 - 6 \] \[ x > -8 \]
Now, we have the solution \( x > -8 \).
The problem states that we need to find the solution set among the given options:
- \( x | x > -8 \)
- The solution set is null.
- \( {3, -8} \)
- \( x | x > 3 \)
Since we found that \( x > -8 \), this means that the set of possible solutions includes all numbers greater than -8.
The correct representation of this solution set would be:
- \( x | x > -8 \), which perfectly matches the first option.
Thus, the answer is:
\( x | x > -8 \)