Question

 

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.

Answer 1

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.

Answer 2

Recall the distributive property:

a(b + c) = ab + ac

Example:

5(2x + 4) = 5 * 2x + 5 * 4 = 10x + 20

Answer 3

Can you do the distributive property on choice A?
What do you get?

A. 4.3(14x+2.5)

Answer 4

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.

Answer 5

@mathstudent55

Answer 6

@carolinar7

Answer 7

@sweetburger @Elsa213 @YanaSidlinskiy @misssunshinexxoxo

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

ty!

Answer 12

sure thing

Answer 13

Just use a calculator for the multiplications with decimals.

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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?

Answer 18

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

Answer 19

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

Answer 20

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.

Answer 21

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.

Answer 22

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

Answer 23

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

Answer 24

Yes

Answer 25

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.

Answer 26

Yes

Answer 27

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

Answer 28

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.

Answer 29

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!

Answer 30

You're welcome.