How do you tell when an equation is an identity? How do you tell when an equation will have no solution? Give an example of both situations.

Question

How do you tell when an equation is an identity?  How do you tell when an equation will have no solution?  Give an example of both situations.

hero · Answer

An equation is an identity when it can be shown that both sides of an equation is equal for all x:

For example

3(5x+2) = 15x + 4
15x + 4 = 15 x +4

If an equation has no solution, then there is no value that can be found for x and the expressions are not equal. For example:

2x + 5 = 2x - 7

Attempting to solve for x:

7 + 5 = 2x - 2x
12 = 0

False