To find the possible values of z and the values that z cannot be based on the statement "The opposite of z is greater than 5," we can start by setting up the inequality:
Opposite of z > 5
1. **Two possible values of z:**
To find two possible values of z, we can solve the inequality for z:
z < -5
So, two possible values of z could be -6 and -10. These values make the statement true since their opposites are greater than 5.
2. **Two values that z cannot be:**
Values that z cannot be are those that do not satisfy the inequality z < -5. Any value of z that makes the opposite of z less than or equal to 5 does not fulfill the given condition. For example, z cannot be 0 or 3 since their opposites are not greater than 5.
3. **What must be true about all possible values of z:**
For all possible values of z, it must hold true that the opposite of z is greater than 5. This means that no matter what value of z you choose, when you take its opposite, that result should be greater than 5. It's a condition that needs to be satisfied by every valid value of z.
