Question

3.
Solve the inequality.





–7 > x > 6


–6 < x < 6


–32 < x < 20

Answer 1

To solve the inequalities provided, let’s analyze each one:

1. **–7 > x > 6**: This can be rewritten as two separate inequalities:
- \( x < -7 \)
- \( x > 6 \)
This means that \( x \) is either less than -7 or greater than 6, which provides two distinct intervals:
- \( (-\infty, -7) \) and \( (6, \infty) \)

2. **–6 < x < 6**: This inequality means:
- \( x \) is greater than -6 and less than 6
This provides a single interval:
- \( (-6, 6) \)

3. **–32 < x < 20**: Similar to the previous one, this means:
- \( x \) is greater than -32 and less than 20
This provides another single interval:
- \( (-32, 20) \)

To summarize:
- The solution to \( -7 > x > 6 \) is: \( (-\infty, -7) \cup (6, \infty) \)
- The solution to \( -6 < x < 6 \) is: \( (-6, 6) \)
- The solution to \( -32 < x < 20 \) is: \( (-32, 20) \)

If you need further steps, like finding intersections or unions between these intervals, please specify!