Question

Find the solution of the linear equation.
2/3 (6 - 3x) = (1 - x) + (3 - x)
A. x = -8
B. x = 8
C. infinitely many solutions
D. no solution

Can someone explain this to me without giving me the answer? I need it step by step. :p

Answer 1

First do you know what to when you have a(b+c)?
Do you know the distributive property?

Answer 2

Yes.

Answer 3

So do that for the left hand side of the equation.

Answer 4

let me know what you get after performing the property

Answer 5

2/3 6 + 2/3 3x?

Answer 6

\[a(b+c)=ab+ac\]
\[\frac{2}{3}(6-3x)=\frac{2}{3}(6)-\frac{2}{3}(3x)\]

I think there was a minus sign in between.

Answer 7

you can write a(b-c) as ab-ac

Answer 8

Now you need to simplify:
\[\frac{2(6)}{3}-\frac{2(3)x}{3}\]

Answer 9

what is 6 divided by 3?

Answer 10

2

Answer 11

\[2(2)-\frac{2(3)x}{3}\]

so instead of 6/3 I will put 2

now what is 3/3?

Answer 12

1

Answer 13

\[2(2)-2(1)x\]

Answer 14

ok instead of 3/3 I put 1

now can you simplify that from there?

Answer 15

mainly you just need to do 2(2) and 2(1) now

Answer 16

How do I do a(b)?

Answer 17

If you can do division you should be able to do the multiplication part.

But let me see if I can explain multiplication...

It is just basically repeated addition.

2(2) means you have 2 groups of 2
or 2+2
which means you have 4 altogether

another example: Pretend we have 5(8)
this means we have 5 groups of 8 (or you can even see it as 8 groups of 5)
Now let's go with the 5 groups of 8
that means we have 8+8+8+8+8 which is 40.

Do you need more help with multiplication? Or more examples?

Answer 18

I found it helpful and made me multiply bigger numbers faster by remembering my time tables.

Answer 19

So 2(2)-2(1)x=?

Answer 20

remember 2(2) means 2+2
and 2(1) means 1+1

Answer 21

You mean like 2^2 and 1^2?

Answer 22

2^2 means 2(2)
1^2 means 1(1)

Answer 23

2^2 means 2(2) which also means 2+2
1^2 means 1(1) which also means 1

Answer 24

but we had 2(1) which means 1+1 which is 2

Answer 25

If you are doing this type of problem, you should have had some experience with multiplication.

Answer 26

Are you sure you don't know how to multiply?

Answer 27

http://www.study-skills-for-all-ages.com/image-files/multiplication_table_1.gif

Here is a multiplication table.
I'm not sure if you ever seen one of these. This makes multiplication faster remembering this table.

Answer 28

I get that now. :) Can you just show me which part to do first? Can you do it step by step with the drawing tool so I can SEE how to do instead of reading it? I think that's what confuses me.

Here's the problem again so I don't have to keep scrolling up. :)

Find the solution of the linear equation.
2/3 (6 - 3x) = (1 - x) + (3 - x)
A. x = -8
B. x = 8
C. infinitely many solutions
D. no solution

Answer 29

we were doing \[\frac{2}{3}(6-3x)\]
we distributed \[\frac{2}{3}(6)-\frac{2}{3}(3x)\]
then you said 6/3=2 and 3/3=1
so we got 2(2)-2(1)x
then I asked you to simplify this part
which is what again?

Answer 30

Come on I already told you what 2(2) and 2(1) is
you should be able to simplify 2(2)-2(1)x

Answer 31

I'm not going to just do the problem for you.
I don't see how that is helpful to you for me to just give you the answer.

Answer 32

I said earlier 2(2)=4 and 2(1)=2
so 2(2)-2(1)x
can be written as 4-2x

so the left hand side of the equation can be written as 4-2x

so the initial equation can be written as 4-2x=(1-x)+(3-x)

I would like to see your attempt on at least simplify the right hand side

Answer 33

the right hand side being (1-x)+(3-x)

Answer 34

2(2)-2(1)=1

Because
2(2) = 2+2
2(1) = 1+1

I know

Answer 35

I'm probably annoying you with this, I'm sorry. :) Now how do I add the x in, where you said 2(2)-2(1)x?

Answer 36

2(2)=4
2(1)=2
so 2(2)-2(1)x
is 4-2x

I already simplified the left hand side
I was asking you to do the right hand side

Answer 37

Even if I asked you to do 2(2)-2(1)
this is not equal to 1

But I didn't ask you to do 2(2)-2(1)

I asked you to do 2(2)-2(1)x

Answer 38

2(2)-2(1) is 4-2
and since 4 and 2 are like terms 4-2 can be simplified more
4-2 is 2

2(2)-2(1)x
is 4-2x
nothing else can be done
4 and 2x are not like terms