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.

Answer 1

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