What is an example of contradiction, a conditional equation, and a identity

I'm doing pre calc in College and I don't know if I learned what ^ that is or if I just forgot, could someone please explain that to me please? Thanks.

contradiction
AN EQUATION THAT HAS NO ANSWERS (NULL SET or NO SOLUTION
3(x+2)=3x-5
3x+6=3x-5
Subtract (3x) from both sides
6=-5
False Statement
No Solution


conditional equation
AN EQUATION THAT IS TRUE BASED "ON THE CONDITION" THAT THE SOLUTION IS X=(A CERTAIN) THAT MAKES THE EQUATION TRUE
3(x+2)=2x-5
3x+6=2x-5
Subtract 3x from both sides AND Subtract 6 from both sides
x=-11
The equation is true based on the condition that x=-11


identity

AN EQUATION THAT HAS ALL REAL NUMBERS AS ITS ANSWERS. At some step in the solving of the equation you will get the same IDENTICAL terms on both sides of the equation.
3(x+2)=3x+6
3x+6=3x+6(Note the same terms on both sides)
COULD STOP HERE and say the solution is ALL REAL NUMBERS
If you Subtract 3x from both sides AND Subtract 6 from both sides you will get
0=0
A TRUE Statement
Solution ::::All Real Numbers

Hi,

x + 5 = x + 23 is a contradiction since 5 does not equal 23.
x + 5 = 23 is a conditional equation that is true only if x = 18.
4(3x + 10) + 8 = 12(x + 4) is an identity since it simplifies to 12x + 48 = 12x + 48 which is true for all real numbers.

5^2 = 5² = 5 x 5 = 25

I hope that helps!! :-)

^ is a carrot and means raised to the power of for example x^2 means x squared.