2x/3=8+4x again...?

Question

I know that x=-2.4.
-----------------------------------------------------------------------------
Ok. I think I understand why I am unable to get this.
-
Many nice people have TRIED HARD to explain this, and I thank you all!
-
BUT!
-
I need sombody to explain this WITHOUT USING NUMBERS! (I think...)
-
In other words instead of saying:
"multiply both sides by 3"...
you could say:
"look for division, and multiply the number to the right (3), by all numbers on the oppisite side. (8 and 4).
-
Because if you say multiply both sides by 3, my brain doesnt understand why, and furthermore cannot face NEW equations with a "both sides by 3" mentality.
-
If your willing to help me (even more). Then when your done, ask yourself:
"Can a eight year old understand this?"
-
Because I am NOT GETTING this at ALL!

Answer 1

Go back and check my response (I just posted) on your original question.

You need to always do the opposite of what's happening...

so... you have 2x/3 = 8 + 4x

Example: Right now, you're dividing by 3 on the left. To get rid of that, do the opposite. (the opposite of dividing by 3 is multiplying by 3). However, you need to do this to BOTH SIDES of the equation.

If the original equation says you're adding on one side, to get rid of it you need to subtract that amount from both sides. And vise versa.

Keep doing this until you get the variable by itself on one side of the equation and everything else on the other side.
------------
It's VERY hard to explain something like this without using numbers for an example. You need to work on transferring the skills yourself... Look at how some of us have worked it out step-by-step (REALLY look at it) and try to understand why we are picking those certain number to do that. WHY do we choose to multiply by 3? (First, why are we MULTIPLYING and second, why are we choosing 3??) WHY do we choose to subtract 12x? (Why are we SUBTRACTING and why are we choosing 12x?)

Answer 2

The main idea behind equations like these is to find the value of the variable, here it is x.First
Let's consider the equation
2x/3=8+4x

This equation is all mixed up.
Our first task is to bring some semblence of order to the equation.
This we do by bringing together all the variable parts to oneside.And all constants to the other side.(Think it like war where all good guys are on one side and the baddies on the other side)
Then after that we try to solve the equation.
Here you should remember that "=" sign is like a border.
If a variable or a constant in the equation crosses over to the other side then the sign of that variable or constant will become the opposite of the original sign it possessed.
For Eg: +1 on crossing "=" becomes -1
-1 on Crossing"=" becomes +1
*1 on crossing "=" becomes /1
/1 on crossing"="becomes *1

So coming to our equation now:

We should bring all the variable parts together

That is 2x should be together with 4x

But 2x is not alone here it has /3 on its side.

So move it to the other side

which will change it according to our earlier explanation to *3.

So multiply the other side by 3.

3*(8+4x)

That will be 24+12x

so now the equation is little simple 2x= 24+12x

But still the good guys and the baddies are all mixed up.

to seperate them bring all good guys on one side and the baddies to the other side.

So move the +12x to the 2x's side.

when 12x crosses "=" it changes it's sign to -12x

so the equation is 2x-12x=24 or -12x+2x=24.

Since 2x and 12x both have the same Variable that is "x"

we will add them (like 12pens adding to 2pens)

adding them will result in -10x (because minus value here is more than the Plus value).

so the whole equation now is -10*x = 24.

Now again the good guys and bad guys have to be seperated.

so move -10 to the other side which will make it -10/

so divide the other side by -10

Which will give -2.4.

THat is x= -2.4.

That's all.

Answer 3

Ok lets see if I can help. This is the first time I've seen this question so apologies if someone has already explained it this way. I think the best way to solve this is to think of the equation like a balance scale where the 'equals' sign is the point of balance.

Let's forget about equations for the moment. Suppose we have a balance scale with 2kg of apples on one side. We could make it balance with, for example 2kg of carrots on the other side. We could then add 0.5kg of flour to one side and as long as we add the same weight to the other side (for example) 0.5kg of sugar, the scales will still balance.

Now lets look at the equation again. On one side of the scale we have 2x/3. This is a bit clumsy to deal with because it is a fraction. But if we were to multiply it by 3 (In other words, make it three times heavier), we would get read of the fraction. So this side of the equation is now 2x. But we've got to keep the equation (scales) in balance, so we will need to multiply the other side by 3 which gives 3(8 + 4x). Multiplying everything inide the brackets by 3 we get 24 + 12x. So our equaion now looks like this :-

2x = 24 + 12x (We've made both sides three times heavier).

If we now take 2x away from the left side this leaves us with 0 on this side. But to keep things in balance, we will need to take 2x away from the other side. So now we have 0 = 24 + 10x. All we need to do now is take 24 away from both sides (to keep it balanced) which leaves -24 = 10x. Finally, we divide both sides by 10 and we get -2.4 = x.

Answer 4

OK ,listen no body is stupid you are very honest and this is a great thing be more confident on your self do not be afraid nothing is difficult in the life but you must concentrate more.
Firstly, we have this equation;2x/3 = 8+4x
we cannot solve it with a number downward(3) all must be straight in one line. So,to delete it we take the 3 and put it in the other side their is a rule which said to take any thing from one side to the other we must change the sign. 3 at the left is divided to travel to the other side it will be times.So, 3X8=24 3X4x=12x
so,the equation must be:2x=24+12x
after that we must make all x in one side and all numbers in the other side,by the rule +12x will go to the other side by minus to be as following: 2x -12x=24
-10x=24
we must have the x alone we apply the rule -10 is times to be in the other side it will be by divided 24/-10=-2.4
So, x=-2.4
hope it help by the way you wish it. Be self confident

Answer 5

Because you have a fraction in the equation, you have to eliminate the bottom number of the fraction (by multiplying). But, if you multiply only one side, you'll change the equation (which you would not like to do.

Once you do this, you'll get 2x=24 +12x
Get x on its own (suppose 2x is 5 and 24 is 3 and 12x is 2. You know that 5=3+2 so 5-2=3)
2x-12x=24
So -10x=24. To get x on its own and thereby solve the equation you have to divide both sides (-10x and 24) by -10 because if you don't, you'll change the equation. And you're left with x=-2.4

Answer 6

OK
when say 2/3 * x that men 2x/3 cause (2*x = 2x )/ 3
so 2x/3 == 2/3 x as you see we separate the x to look good only

so

2/3 x = 8 + 4x

as we know you only + Xs together and Numbers togethers
you cant + : 8 + 4x >>> cause 8 is not X, and 4x is not a number only

so

2/3 x = 8 + 4x we move Xs together in one side and numbers the other side

2/3 x = 8 + 4x --> 2/3 x - 4x = 8

why 4x now is ( - 4x ) ?
cause the number or an X moved from aside to the other side, it will change it sign 4x was +, now -

so

2/3 x - 4x = 8 by calculator we get ( 2/3 = 0.66)
0.66 x - 4 x = 8 by calculator we get ( 0.66 - 4 = 3.34 )

so 3.34 x = 8

to get the x you have to make the x alone in a side do you get that?
so remove the 3.34 from the x side is by div. all side by 3.34
and it look like that

(3.34 / 3.34) x = 8 / 3.34by calculator we get
1/1 x = 2.39 --> x = 2.39 OR x = 2.4

Answer 7

2x/3 = 8 + 4x

3(2x/3) = 3(8) + 3(4x)

2x = 24 + 12x

2x - 2x = 24 + 12x - 2x

0 = 24 + 10x

0 - 24 = 24 + 10x - 24

- 24 = 10x

- 24/10 = 10x/10

- 24/10 = x

- 2 4/10 = x

- 2 2/5 = x

- 2.4 = x

The answer is x = - 2.4

Insert the x value into the equation

- - - - - - - - - - - - - - - - - - - - - -

2x/3 = 8 + 4x

2(- 2.4)/3 = 8 + 4(- 2.4)

- 4.8/3 = 8 + (- 9.6)

-1.6 = 8 - 9.6

- 1.6 = - 1.6

- - - - - - - - - - - - -s-

Answer 8

2x/3=8+4x
2x=8(x3)+4x(x3) because 3on the other side is divide, when you move 3, then you have to chang it too multiply.

Then you'll get 2x=24 +12x when you move 12x to the other side so 12x will become negative.
2x-12x=24
-10x=24
x=24÷-10
x=-2.4

Answer 9

2x/3 = 8+4x

you want that x by itself on one side
its being divided by 3 so do the opposite to both sides (multiply by 3)

(2x/3) * 3 = (8+4x) * 3 =
2x = (3* 8) + (3*4x) =
2x = 24 + 12x

you want the x by itself on one side so you know what it equals
its being multiplied by 2 so do the opposite to both sides (divide by 2)

2x/2 = 24/2 + 12x/2
1x = 12 + 6x

again you want the x by itself on one side so combine the x's by doing the opposite -- + 6x is on one side, - 6x to move it to the other side.

1x - 6x = 12 + 6x - 6x
-5x = 12

you want the x by itself, its being multipled by -5 so do the opposite to move it over (divide by -5)

-5x/-5x = 12/-5x
x= - 2.4

plug the answer back into the original equation to check your work, if both sides are equal then you did it right.

2x/3 = 8 + 4x
x= - 2.4
2(-2.4)/3 = 8 + 4(-2.4)
-4.8/3 = 8 + -9.6
-1.6 = -1.6

the equation balances so the value of x was correct