Solutions after expanding

The question

3(3x + 1) = 9x + 3

How many solutions?

3(3x + 1) = 9x + 3

x is gone

3 = 3is true

infinitely many solutions

Collect the x terms on one side and see what is left.
First multiply out the bracket.
Both sides have the same number of x, so taking it off both sides removes x completely.
What is left is 3 = 3, 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
First multiply out the bracket.
03
Both sides have the same number of x, so taking it off both sides removes x completely.
04
What is left is 3 = 3, which is true whatever x is. So every number works — infinitely many solutions.