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GenericNoodles
 one year ago
Algebra 1 question!
Consider the equation 3x^2+x= (X2)(X5)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.
GenericNoodles
 one year ago
Algebra 1 question! Consider the equation 3x^2+x= (X2)(X5)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.

This Question is Closed

GenericNoodles
 one year ago
Best ResponseYou've already chosen the best response.1I don't understand how to use the properties to alter the equation, nothing too big I hope :)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3It'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
 one year ago
Best ResponseYou've already chosen the best response.3Just find a multiplication in your equation, and change the order of the factors.

GenericNoodles
 one year ago
Best ResponseYou've already chosen the best response.1I'm gonna give it a go haha. 3x^2+X (2x)(X5)x

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3No. 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
 one year ago
Best ResponseYou've already chosen the best response.3Remember to write everything else exactly as i was including the equal sign.

GenericNoodles
 one year ago
Best ResponseYou've already chosen the best response.1I see what you mean! So it's (5X)(2X) correct?

GenericNoodles
 one year ago
Best ResponseYou've already chosen the best response.1i flipped those on accident, lol. (X5)(X2)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3It 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= (X2)(X5)x This is what I was going for: 3x^2+x= (X5)(X2)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 (X2)(X5)x, and now it's (X5)(X2)x

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Since all that changed was the order oft he multiplication, that is an application of the commutative property. That takes care of part A.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Part A. 3x^2+x= (X5)(X2)x Ok so far?

GenericNoodles
 one year ago
Best ResponseYou've already chosen the best response.1I'm sorry for the confusion, it's been a long day! 3x^2+X=(X5)(X2) Associative is putting them into groups yes?

GenericNoodles
 one year ago
Best ResponseYou've already chosen the best response.1So (3x^2)+x= (X5)(X2)? I'm not sure really.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Wait. For part A., you are correct just above, but don't forget the x at the end of (x5)(x2)x

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Now 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
 one year ago
Best ResponseYou've already chosen the best response.3For 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
 one year ago
Best ResponseYou've already chosen the best response.1So would I just change the order of (X5)(X2) to (5x)(2X)X?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3If 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
 one year ago
Best ResponseYou've already chosen the best response.3That 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
 one year ago
Best ResponseYou've already chosen the best response.3Finally we need to do part C. Now we start with the result of part B. 3x^2+x= x(x  5)(x  2)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3The 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
 one year ago
Best ResponseYou've already chosen the best response.3That is it. This whole problem is just an exercise in using the commutative, associative, and distributive properties.

GenericNoodles
 one year ago
Best ResponseYou've already chosen the best response.1I 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!
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