I'm trying to learn the difference between conditional and identity equations. Can you please check my work??

Question

12). 3(x+2)=5x+4. I said conditional because on the one side x needed to equal negative two while on the other, it needed to equal -.8.

15). (4x+1)-2x=2(x+2) I said identity.
18). x^2+2(3x-2)=x^2+6x-4. I said Conditional, out of more of a guess than actual information. I reduced it to x^2+x=.60, but I was unsure how to figure out the left side of the reduction. Could you explain this??

Thanks!!!

Answer 1

18.
x^2+2(3x-2)=x^2+6x-4
x^2 + 6x - 4 = x^2 + 6x - 4
clearly an identity, that is, the equation is true for all values of x

15.
(4x+1)-2x=2(x+2)
4x + 1 - 2x = 2x + 4
2x + 1 = 2x = 4
1 = 4 , Oh really?

This equation has no solution.
It is neither an identity nor "conditional equation".