Check if input is not integer or number at all cpp

I've created a guessing game where you have to guess randomly generated number in range from 1 to 100. I also managed to restrict a user if they enter a number that is out of the range, and requires new input. The problem is when you accidentally enter letters or symbols. Then it enters an infinite loop. I tried:

while(x<1 || x>100 || cin.fail())//1. tried to test if input failed (AFAIU it checks if input is expected type and if it is not it fails)
while(x<1 || x>100 || x>='a' && x<='z' || x>='A' && <='Z') // 2. tried to test for letters at least
while(x<1 || x>100 x!=(int)x)//3. to test if it is not integer
{ cout<<"Out of range";
  cin>>x;
}