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No Solution & Identity

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No Solution & Identity

More with variables on both sides

Click on the screen to proceed through this lesson.

- Not every equation has a solution…like x = 5
- Sometimes you’ll get 5 = 9
- This is false… 5 ≠ 9
- We’ve lost the variable
- The answer is type of equation is NO SOLUTION

18x – 5 = 3(6x – 2)

18x – 5 = 18x – 6

-18x-18x

-5 = -6

False… therefore the answer is:

No Solution

a – 4a = 2a + 1 – 5a

-3a = -3a + 1

+3a+3a

0 = 1

False… therefore the answer is:

No Solution

- Sometimes you’ll get 5 = 5
- This is a true statement
- But…we’ve lost the variable.
- The answer to this equation is IDENTITY
- This means you may pick any number for the variable and it will make a true statement when you check your answer.

14 – (2x + 5) = -2x + 9

14 – 2x – 5 = -2x + 9

9 – 2x = -2x + 9

+2x+2x

9 = 9

True… therefore the answer is:

Identity

- Since the solution to
4 – (2x + 5) = -2x + 9

is Identity…you may pick any number for x to check. All real numbers are possible solutions.

y – 5 = -(5 – y)

y – 5 = -5 + y

-y -y

-5 = -5

True… therefore the answer is:

Identity