equations? math?

Question

2x/3=8+4x
-
solve for x.
-
Keep in mind that I fail to "grasp" this even after several attempts.
I know I have "move" things like a scale.
-
But I never know WHAT or in WHAT way!
-
Should I subtract 2 from both sides?
multiply 3 on both sides?
add 4?
subtract 8?
add 8?

I am having SERIOUS trouble "getting" this.
Please help me UNDERSTAND this so I can look back and laugh at how hard this is for me.
-
PLEASE try a different way to explain this, other than the conventional ways that are allways taught, because they have done NO GOOD for ME!
-
If somebody wants to take the time... I will converse through email or Yahoo! IM.
-
PLEASE HELP ME! - I want to pass my GED, but I can't get this.
-
Thank you in advance for your help.
-
If you think you can take a few minutes to explain this to me then leave your IM name, and I will IM you.

Answer 1

chose any way you like of 2 ways

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

way 1
--------------
2/3 x - 4x = 8
x ( 2/3 - 4) = 8
x ( 2/3 - 4/1) = 8
x ( (1*2 -3*4) /3 ) = 8
x 10/3 = 8
x = (8*3) / 10
x = 2.4
---------------
way 2
--------------
2/3 x - 4x = 8
x ( 2/3 - 4) = 8
x ( 0.66 - 4 ) = 8
x 3.34 = 8
x = 8 / 3.34
x = 2.39
x = 2.4

Answer 2

First thing, multiple both sides by 3. This is not NECESSARY, but it makes it EASIER by getting rid of the fractions.

That works out to 2X = 24 + 12X.

If you look at that a moment, you see that each term is divisible by 2, so again just to make things EASIER, divide both sides by 2.

That leaves

X = 12 + 6X

Your goal from here is to come up with an equation of the form

SOMETHING * X = - SOMETHINGELSE,

after which it is obvious that

X = - SOMETHING/SOMETHINGELSE and you are done.

I put that minus sign in there because it is customary for the step before that to be

SOMETHING * X + SOMETHINGELSE = 0. For reasons that become more apparent in slightly more advanced studies, it's just convenient to have a standard form in which one side of the equation is 0.

In your case this is 5 X + 12 = 0, so X = -12/5

Remember, there is no "One True Correct Series of Steps", as I illustrated by mentioning that some of the steps I recommended weren't absolutely necessary.

Hope this helps!

Answer 3

2x/3=8+4x

The left side is "divided by 3" so let's get rid of that. You do so by doing the opposite on both sides... in this case, multiplying by 3.

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

the 3 on top and bottom cancel on the left:
2x = 3(8+4x)

Now distribute the 3 through the parentheses on the right:
2x = 3(8) + 3(4x)
2x = 24 + 12x

Now you want all the x on one side. So, let's move the 12x to the left. Right now, we're adding 12x on the right side. Doing the opposite, we need to subtract 12x from each side:
2x - 12x = 24 + 12x - 12x
2x - 12x = 24

We can combine the like terms of 2x and 12x. 2-12 = -10, so we're left with:
-10x = 24

Now we need to get rid of that -10 to get x alone... Since we're multiplying by -10, we need to divide by -10 on both sides.

-10x/-10 = 24/-10

the -10 cancels on the left:
x = 24/-10
x = -2.4

If you still need more help, you can email me. My email is [e-mail]

Answer 4

You have to bear in mind 2 things:
1. you need to end up with a single 'x' on one side of the equation
2. whatever you do to one side of the equation, you must do to the other.

So you could start by multiplying each side by 3 to give:
2x = 3(8+4x) = 24 + 12x

then divide each side by 2 to give:
x = (24 + 12x)/2 = 12 + 6x

now you have x on both side, and you need x on only one side, so subtract x from each side:
0 = 12 + 5x

now subtract 12 from each side:

-12 = 5x

now divide by 5:

-12/5 = x

so x = -12/5 = -2.4

(but this is not the only way or necessarily the quickest way to do it)

Answer 5

1. multiply both side by 3, so that fraction is eliminated
2. subtract 12x from 2x
3. divide the 24 by the numerical coefficient of the difference above, or more correct multiply the reciprocal of the numerical coefficient of the difference in (2)

ans: x= - 12/5

Answer 6

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 7

I agree on flongkoy's answer..:)
his right;)