Thanks @lgbasallote , brain fart :)
Any two sides when added have to be greater than the third side.
Therefore, AB + BC > CA
If it was B then AB + AC = CA
No.
AB + BC > CA
7 + 5 > CA
12 > CA
Possible equations:
12 > 2
12 > 5
12 > 12
12 > 13
It's not 12 or 13, because 12 isn't greater than itself, and 12 isn't greater than a large number. Now, since CA = 2 or 5:
AB < BC + CA (again, two sides added up are greater than the third)
7 < 5 + 2
7 < 7
7 < 5 + 5
7 < 10
7 can't be less than itself. 7 is less than 10, so you know 5 is the answer.
Here.
x < 5 + 7
x + 5 > 7
x < 12
x > 2
Therefore, you know that the set of numbers possible are \(2 < x < 12\). Which of those numbers is within that range?