Number of solutions

The question

17x + 25 = 25 + 17x

How many solutions?

17x + 25 = 25 + 17x

x is gone

25 = 25is true

infinitely many solutions

Collect the x terms on one side and see what is left.
Both sides have the same number of x, so taking it off both sides removes x completely.
What is left is 25 = 25, which is true whatever x is. So every number works — infinitely many solutions.

How it works.

01
Collect the x terms on one side and see what is left.
02
Both sides have the same number of x, so taking it off both sides removes x completely.
03
What is left is 25 = 25, which is true whatever x is. So every number works — infinitely many solutions.