The solution set is
![c \geq 5](https://tex.z-dn.net/?f=c%20%5Cgeq%205)
, meaning that all
![c](https://tex.z-dn.net/?f=c)
at least
![5](https://tex.z-dn.net/?f=5)
satisfy this constraint.
If
![c=5](https://tex.z-dn.net/?f=c%3D5)
, we have
![x < 5](https://tex.z-dn.net/?f=x%20%3C%205)
and
![x > 5](https://tex.z-dn.net/?f=x%20%3E%205)
, meaning
![x](https://tex.z-dn.net/?f=x)
has to be both greater than and less than
![5](https://tex.z-dn.net/?f=5)
, which is impossible. If
![c](https://tex.z-dn.net/?f=c)
is any greater,
![x > c > 5](https://tex.z-dn.net/?f=x%20%3E%20c%20%3E%205)
, so
![x](https://tex.z-dn.net/?f=x)
still must be greater and less than
![5](https://tex.z-dn.net/?f=5)
at the same time. So for all
![c \geq 5](https://tex.z-dn.net/?f=c%20%5Cgeq%205)
, the system
![x < 5, x > c](https://tex.z-dn.net/?f=x%20%3C%205%2C%20x%20%3E%20c)
has no solution.
Consider the given equation to be f(x) whose first derivative is positive for all real x. This implies f(x) is a strictly increasing function. Thus it has only 1 root.
Net 2....................