There are three basic kinds of sequations:

1. Conditional equations
2. Identity equations
3. Contradiction equations

Conditional equations are true for some values of the variable, say x,
and false for others.

2x + 1 = 7  is true when 3 is substituted for x

2(3) + 1 = 7
   6 + 1 = 7
       7 = 7

However

2x + 1 = 7  is false when 4 is substituted for x

2(4) + 1 = 7
   8 + 1 = 7
       9 = 7

and that's false.



An identity is an equation in a variable, say x, such that every value
of x makes it true.

Here is a simple identity

x + x = 2x

Any value you sustitute for x will make it true.

If you substitute x = 17 it is true

17 + 17 = 2(17)
     34 = 34

If you substitute x = 1 it is true:

1 + 1 = 2(1)
    2 = 2

If you substitute -31.791 it is true:

-31.791 + (-31.791) = 2(-31.791)

            -63.582 = -63.582

Here's a more complicated identity:

(x-1)² + 3x² + 8 = (2x-3)² + 10x

Substitute random numbers for x.  You'll see that
 
it is always true


-------------------------------------


Equations that are never true are called "contradiction equations":

Here;'s a contradiction equation:

3x = x + 2x + 7

Edwin