SOLUTION: I need to identify each equation as being an identity, contradiction, or conditional equation. I need to verify my solution. Here is my problem: 5x + 2 - 2x + 3 = 7x + 2 - x + 5

Algebra ->  Linear-equations -> SOLUTION: I need to identify each equation as being an identity, contradiction, or conditional equation. I need to verify my solution. Here is my problem: 5x + 2 - 2x + 3 = 7x + 2 - x + 5      Log On


   

Question 213989: I need to identify each equation as being an identity, contradiction, or conditional equation. I need to verify my solution. Here is my problem:
5x + 2 - 2x + 3 = 7x + 2 - x + 5
I feel like I'm way over my head. Please help!
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
I need to identify each equation as being an identity, contradiction, or conditional equation. I need to verify my solution. Here is my problem:

5x+%2B+2+-+2x+%2B+3+=+7x+%2B+2+-+x+%2B+5+

5x+%2B+2+-+2x+%2B+3+=+7x+%2B+2+-+x+%2B+5+ Rearranging to collect x terms and numbers will yield

5x-2x%2B2%2B3=7x-x%2B2%2B7

3x%2B5=6x%2B9

Subtract 3x from both sides of equation to get x terms on right side

3x%2B5-3x=6x%2B9-3x

5=3x%2B9

Subtract 9 from both sides to get a number on left side and isolate x term

5-9=3x%2B9-9

-4=3x

Divide 3 to both sides of equation

-4%2F3=3x%2F3

x=-4%2F3

Let's verify the solution by substituting x=-4/3 into simplified equation below

given as 5x+%2B+2+-+2x+%2B+3+=+7x+%2B+2+-+x+%2B+5+ or simplifying 3x%2B5=6x%2B9

3%2A%28-4%2F3%29%2B5=6%2A%28-4%2F3%29%2B9}

Now check to see if left side = right side. If it is then it's an identity.

-4%2B5=2%2A%28-4%29%2B9

1=-8%2B9

1=1 So this is an identity and we can say that the solution is x=-4%2F3

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J