2x+1=2x+1 is an example of an identity that has an infinite amount of solutions

Yes. 2x+1 is equals to 2x+1 which means that it has an infinite amount of solutions.

The only way it doesn't have an infinite amount of solutions is if the result is different.

For example, 4x - 4 = 8

The - 4 goes on the other side which turns it into + 4.

4x = 12

Divide by 4 on both sides.

This gives you x = 3.

This is an example of only one solution.

2x+3 = x+3

2x+3 is not equal to x+3.

So this is a no solution.

3x+6+2x = 5x+6

Add the like terms together.

3x+2x+6 = 5x+6

5x+6 = 5x+6

This statement is true, 5x+6 is equal to 5x+6.

So this is an infinite amount of solutions.