I don't remember much from Trig but K Stands for an integer so 1,2,3, etc. The Cos wave has many solutions because of it being a wave. So first you find one solution and then add 2kPi for the rest of the answers.
Haha, it's not even algebra, it's trigonometry. Learn basic math before you try correcting people. k stand for any real integer number. If you knew anything about trig or the unit circle you'd know that even though cos(x)=1/2 appears on two point around the unit circle, you can go around again again and reach the same two points continuously. Therefore, there's an infinite amount of values which x can be.