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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
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Equations that are never true are called "contradiction equations":
Here;'s a contradiction equation:
3x = x + 2x + 7
Edwin
