Which two expressions are equivalent?
A. 4.3(14x+2.5)
B. 14(4.3x+2.5)
C. 20.6x+28+39.6x+7
D. 60.2x+2.5
Medal and fan for best answer. I am not good at figuring out equivalent expressions.

- anonymous

- katieb

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- mathstudent55

You need to use the distributive property in each choice A and B.
Combine like terms in choice C.
Then compare all results including choice D.

- mathstudent55

Recall the distributive property:
a(b + c) = ab + ac
Example:
5(2x + 4) = 5 * 2x + 5 * 4 = 10x + 20

- mathstudent55

Can you do the distributive property on choice A?
What do you get?
A. 4.3(14x+2.5)

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## More answers

- anonymous

Ok so I have 4.3*2.5, but i'm having trouble multiplying 4.3 *14x. I can't seem to figure out how to multiply with the variable number multiplication thingy.

- anonymous

- anonymous

- anonymous

- anonymous

Anyone? I would like help plz. My schoolwork is taken me all day and I wanna b done with it.

- jim_thompson5910

to multiply 4.3 *14x, you drop the x for now and just evaluate 4.3 *14
you then tack on x to the answer

- jim_thompson5910

example: 2*8x = 16x because 2*8 = 16

- anonymous

ty!

- jim_thompson5910

sure thing

- mathstudent55

Just use a calculator for the multiplications with decimals.

- mathstudent55

A. 4.3(14x+2.5) = 4.3 * 14x + 4.3 * 2.5
Use a calculator for 4.3 * 14 and for 4.3 * 2.5

- mathstudent55

A. 4.3(14x+2.5) = 4.3 * 14x + 4.3 * 2.5 = 60.2x + 10.75

- mathstudent55

You can tell already that A and D are not the same.

- mathstudent55

Now let's try B. We need to distribute again.
B. 14(4.3x+2.5) = 14 * 4.3x + 14 * 2.5
Can you finish the expression above by doing the two multiplications?

- anonymous

I got 95.2 by adding the sums of the two multiplications.

- mathstudent55

No. You can add the two quantities. One has x and one has no x. The are not like quantities, so you can add them.
B. 14(4.3x+2.5) = 14 * 4.3x + 14 * 2.5 = 60.2x + 35

- mathstudent55

So far we have:
A. 60.2x + 10.75
B. 60.2x + 35
C.
D. 60.2x + 2.5
None of them are equivalent.
We must find what C is equal to.

- mathstudent55

C. 20.6x+28+39.6x+7
You can only combine like terms.
Terms with x are like terms. You can combine them together.
Terms with no x are like terms. You can combine them together.
You cannot combine together terms with x and terms without x.

- mathstudent55

Examples:
2x + 5x = 7x
2 + 5x = 2 + 5x
5 + 2x + 3 + 4x = 5 + 3 + 2x + 4x = 8 + 6x

- mathstudent55

Do you understand the idea of like and unlike terms now?

- anonymous

Yes

- mathstudent55

Let's try C. now.
First we move the like terms together. Then we combine like terms.
C. 20.6x+28+39.6x+7 = 20.6x + 39.6x + 28 + 7
Ok so far? All I did was rearrange the terms.

- anonymous

Yes

- mathstudent55

Now we combine the like terms with x: 20.6x + 39.6x = 60.2x
and we combine the like terms without x: 28 + 7 = 35
We get:
C. 20.6x+28+39.6x+7 = 20.6x + 39.6x + 28 + 7 = 60.2x + 35

- mathstudent55

Now we can write what all the choices are equal to:
A. 60.2x + 10.75
B. 60.2x + 35
C. 60.2x + 35
D. 60.2x + 2.5
Now it's obvious which 2 expressions are equivalent.

- anonymous

Ty for your help and sry I went in and out of the conversation. There is a weird glitch that wont let me type after I send a reply. Thank you!

- mathstudent55

You're welcome.

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