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# No Solution & Identity - PowerPoint PPT Presentation

No Solution & Identity. More with variables on both sides Click on the screen to proceed through this lesson. Tricky Questions…. 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

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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

No Solution

a – 4a = 2a + 1 – 5a

-3a = -3a + 1

+3a+3a

0 = 1

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

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