If I solve an equation and it comes out to all real numbers, is going to be always true, sometimes true, or never true?
I do not know why I am having trouble with this but really need help.
If your equation has the solution of all real numbers, then your equation is an "identity".
here are the different cases for linear equations:
case 1: one unique solution
3x -4 = 2x + 1
3x-2x = 1+4
x = 5
case 2: no solution
3x - 4 = 3x - 5
3x-3x = -5+4
0 = -1 , which is a false statement, thus NO solution
case 2: all real numbers work
3x - 12 = 3(x-4)
3x - 12 = 3x - 12
0 = 0 , which is a true statement
in general , if the variable drops out, and you end up with a false statement, there is no solution
if the variable drops out, and you end up with a true statement, there will be an infinite number of solution and your equation is an identity.
The same would apply to second degree equations and higher, except you could have 2, 3 or more solutions.
the cases 2 and 3 would still apply.