How many solutions are there to this equation?

Question

7x - 3(x -1) = 2(2x + 3)

Answer 1

7x-3(x-1)=2(2x+3)

7x-3x+3=4x+6

4x+3=4x+6

4x-4x=6-3

0=3 False

There is no x to satisfy this equation since 0 is not equal to 3

Answer 2

Answer 3

7x-3x+3 = 4x +6

4x + 3 = 4x + 6

3 = 6

whatever value x is, the equation is false

Usual answer would be zero solutions, or the null set

But you could also say infinity or negative infinity, since infinity+a finite number = infinity + a different finite number. Same with negative infinity. But since infinity itself is a limit, not a number, it's traditional to just say there is no solution. Still infinity and negative infinity are solutions