Question

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.

Answer 1

I don't understand how to use the properties to alter the equation, nothing too big I hope :)

Answer 2

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)

Answer 3

Just find a multiplication in your equation, and change the order of the factors.

Answer 4

I'm gonna give it a go haha.

3x^2+X (2-x)(X-5)x

Answer 5

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.

Answer 6

Remember to write everything else exactly as i was including the equal sign.

Answer 7

I see what you mean! So it's (5-X)(2-X) correct?

Answer 8

i flipped those on accident, lol. (X-5)(X-2)

Answer 9

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

Answer 10

Since all that changed was the order oft he multiplication, that is an application of the commutative property.
That takes care of part A.

Answer 11

Part A.
3x^2+x= (X-5)(X-2)x

Ok so far?

Answer 12

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?

Answer 13

So (3x^2)+x= (X-5)(X-2)? I'm not sure really.

Answer 14

Wait.
For part A., you are correct just above, but don't forget the x at the end of (x-5)(x-2)x

Answer 15

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.

Answer 16

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.

Answer 17

So would I just change the order of (X-5)(X-2) to (5-x)(2-X)X?

Answer 18

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.

Answer 19

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)

Answer 20

Finally we need to do part C.
Now we start with the result of part B.

3x^2+x= x(x - 5)(x - 2)

Answer 21

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)

Answer 22

That is it.
This whole problem is just an exercise in using the commutative, associative, and distributive properties.

Answer 23

Sorry, but gtg.

Answer 24

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!

Answer 25

yw