Show that the solution to the following recurrence is O(n lg n)

* There is a solution to this problem here on Chegg but I am confused about two things. First, why on line 4 of the substitution phase does the equality suddenly become an inequality for two lines? Second, how are they left with cn lg n? I don't see how they are getting rid of the rest of the terms.

Here is the substitution portion of the solution: