Given
The compound inequalities ...
- x > 9 and x < 9
- x < 9 or x > 9
- x ≥ 9 and x ≤ 9
- x ≤ 9 or x ≥ 9
Find
A verbal description of each of them
Solution
This is asking you to describe in words what the statement says using math symbols. It is a test of reading comprehension.
1. How would you describe the set of numbers that is both greater than 9 and less than 9? There are no such numbers. The solution to that compound inequality doesn't exist.
2. How would you describe the set of numbers that is either greater than 9 or less than 9? That's almost every number. The only number that is not in that set is the number 9 itself. The solution to that compound inequality is all real numbers except 9.
3. How would you describe the set of numbers that is both ...
- greater than or equal to 9
- less than or equal to 9.
The only number that meets both these conditions is the number 9. The solution to that compound inequality is the number 9 only.
4. How would you describe the set of numbers that is either of ...
- greater than or equal to 9
- less than or equal to 9.
That is, it is any number that is less than 9, equal to 9, or greater than 9. It is essentially any number. The solution to that compound inequality is all real numbers.
