GenericNoodles
  • GenericNoodles
Algebra 1 question! Consider the equation 3x^2+x= (X-2)(X-5)x A. Use the commutative property to create an equation with the same solution set. B. Using the result from part A, use the associative property to create an equation with the same solution set. C. using the results from part b, use the distributive property to create an equation with the same solution set.
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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GenericNoodles
  • GenericNoodles
I don't understand how to use the properties to alter the equation, nothing too big I hope :)
mathstudent55
  • mathstudent55
It's easier that you think. The commutative property is that you can change the order of the factors in a multiplication without changing the answer. Examples: ab = ba 5 * 4 = 4 * 5 (x + 1)(x - 3) = (x - 3)(x + 1)
mathstudent55
  • mathstudent55
Just find a multiplication in your equation, and change the order of the factors.

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GenericNoodles
  • GenericNoodles
I'm gonna give it a go haha. 3x^2+X (2-x)(X-5)x
mathstudent55
  • mathstudent55
No. When you changed from x - 2 to 2 - x, you actually changed the factors. x - 2 is not the same as 2 - x. Keep x - 2 exactly as it is. Just change the order of the factors x - 2 and x - 5.
mathstudent55
  • mathstudent55
Remember to write everything else exactly as i was including the equal sign.
GenericNoodles
  • GenericNoodles
I see what you mean! So it's (5-X)(2-X) correct?
GenericNoodles
  • GenericNoodles
i flipped those on accident, lol. (X-5)(X-2)
mathstudent55
  • mathstudent55
It is by accident, but DO NOT CHANGE the content of each factor. Keep x - 2 and x - 5 as they are. Original equation: 3x^2+x= (X-2)(X-5)x This is what I was going for: 3x^2+x= (X-5)(X-2)x See how x - 2 remains as x - 2 and x - 5 remains as x - 5? What did change is that the right side was originally (X-2)(X-5)x, and now it's (X-5)(X-2)x
mathstudent55
  • mathstudent55
Since all that changed was the order oft he multiplication, that is an application of the commutative property. That takes care of part A.
mathstudent55
  • mathstudent55
Part A. 3x^2+x= (X-5)(X-2)x Ok so far?
GenericNoodles
  • GenericNoodles
I'm sorry for the confusion, it's been a long day! 3x^2+X=(X-5)(X-2) Associative is putting them into groups yes?
GenericNoodles
  • GenericNoodles
So (3x^2)+x= (X-5)(X-2)? I'm not sure really.
mathstudent55
  • mathstudent55
Wait. For part A., you are correct just above, but don't forget the x at the end of (x-5)(x-2)x
mathstudent55
  • mathstudent55
Now for part B, you need the associative property. The associative property states that you can change the grouping in a multiplication without changing the answer.
mathstudent55
  • mathstudent55
For part B, you start with the answer to part A. Let's start with this: 3x^2+x= (x - 5)(x - 2)x Now we use the associative property.
GenericNoodles
  • GenericNoodles
So would I just change the order of (X-5)(X-2) to (5-x)(2-X)X?
mathstudent55
  • mathstudent55
If you look on the right side, according to the order of operations (you may know it as PEMDAS), we do multiplications in the order they appear from left to right.
mathstudent55
  • mathstudent55
That means you'd do first (x - 5) times (x - 2), then multiply the result by x. That means x - 5 is grouped with x - 2. Then you multiply by x. To change the grouping, just write the x first. Then you'll be grouping the x with x - 5. That is a change of grouping. Part B. 3x^2+x= x(x - 5)(x - 2)
mathstudent55
  • mathstudent55
Finally we need to do part C. Now we start with the result of part B. 3x^2+x= x(x - 5)(x - 2)
mathstudent55
  • mathstudent55
The distributive property is: a(b + c) = ab + ac or in reverse ab + ac = a(b + c) We use the reverse on the left side to factor out an x. Part C. x(3x + 1)= x(x - 5)(x - 2)
mathstudent55
  • mathstudent55
That is it. This whole problem is just an exercise in using the commutative, associative, and distributive properties.
mathstudent55
  • mathstudent55
Sorry, but gtg.
GenericNoodles
  • GenericNoodles
I really appreciate you explaining this out to me! I didn't catch it in class but it's very clear to me now. Thank you!
mathstudent55
  • mathstudent55
yw

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