I need some help understanding clearing fractions. Example: -x+2/5=5-4/3x

- anonymous

I need some help understanding clearing fractions. Example: -x+2/5=5-4/3x

- chestercat

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- anonymous

-x+2/5=5-4/3x

- anonymous

Is the equation
a) \(-x + \frac{2}{5} = 5 - \frac{4}{3x}\)
b) \(\frac{-x + 2}{5} = 5- \frac{4}{3x}\)
c) None of the above.

- anonymous

a)

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## More answers

- anonymous

the x is not below the 4

- anonymous

oh, good. That's even better.

- anonymous

\[-x + \frac{2}{5} = 5 - \frac{4}{3}x\]

- anonymous

Right?

- anonymous

Yes

- anonymous

Ok, so lets start by getting all of our 'like' terms to have the same denominator. To do that, we'll make the -x into a fraction with a 3 on bottom. How can we do that?

- anonymous

-x/3

- anonymous

Nearly, but it must maintain equivalence. 3/3 is 1 right?

- anonymous

-1x/3

- anonymous

No. Stop guessing and listen. 3/3 = 1. Right?

- anonymous

yes

- anonymous

Ok, and 1 times any number gives you the same number right?
a*1 = a

- anonymous

right

- anonymous

so then:
\[a = 1*a = \frac{3}{3}*a = \frac{3a}{3} = a\]

- anonymous

Did you follow that? Sometimes it's hard to read on one line.

- anonymous

yes

- anonymous

Ok, so what is -x as a multiple of 1/3?

- anonymous

The basic rule of thumb for equivalent fractions is:
You can multiply the top and bottom by the same thing and the value doesn't change.

- anonymous

don't know

- anonymous

So we have:
\[\frac{-x}{1}\]
And we want to get a 3 on the bottom, so we multiply the bottom times 3. That means we have to multiply the top by 3 also to keep it having the same value as -x.

- anonymous

\[\frac{-3x}{3} = -x\] Right?

- anonymous

-3x/3

- anonymous

Right.

- anonymous

So lets do the same thing to the 5 on the right side of the equation. We need to get a 5 on bottom, so what would it be.. We have:
\[\frac{5}{1}\]

- anonymous

5/1+2/5

- anonymous

Ok, we have this (after changing the denominator on -x)
\[\frac{-3x}{3} + \frac{2}{5} = 5 -\frac{4x}{3}\]

- anonymous

Can you use algebra to get all the terms with x on one side, and all the terms without x on the other?

- anonymous

I appreciate you trying to help me, but I need to see the example I gave solved from the beginning to the end. It isn't working very well showing me a step here and there.

- anonymous

Hello

- anonymous

One second.

- anonymous

Starting from \[\frac{-3x}{3} + \frac{2}{5} = 5 - \frac{4x}{3}\]
Can you solve for x?

- anonymous

James are you there?

- anonymous

-x+2/5=5-4x/3

- anonymous

Because you have denominators and an = sign, you need to find a common denominator.
What is the common denominator using 5 and 3

- anonymous

15

- anonymous

So multiply the whole equation by 15.

- anonymous

Yes.. every term.

- anonymous

15(-x+2/5)=15(5-4/3x)

- anonymous

Yep. And distribute.

- anonymous

(15)(-x) + (15)(2) (15)(5) - (15)(4x)
----- = -------
5 3

- anonymous

Cancel out the denominators into the numerators.

- anonymous

(15)(-x) + (3)(2) = (15)(5) - 5(4x)

- anonymous

-15x + 6 = 75 - 20x

- anonymous

Now solve for x in the usual way.

- anonymous

Blexting, let him do it.

- anonymous

I don't know

- anonymous

James when you are solving and you see x's on both sides of the equation, I like to get rid of the smallest one.
Which one is smaller -15x or -20x

- anonymous

-20x

- anonymous

so add 20x to both sides

- anonymous

James, if you have an equation:
5x + 4 = 4
How do you solve for x?

- anonymous

What do you get James when you +20x to both sides?

- anonymous

20x-15x+6=75-20x=20X

- anonymous

THE LAST ONE should be a plus sign

- anonymous

Good so add like terms.

- anonymous

-5x+6=75-x

- anonymous

20x - 15x (20 - 15 = ?)

- anonymous

-20x + 20x = (-20 + 20 = ?)

- anonymous

5

- anonymous

So you have
5x + 6 = 75 (because your -20 + 20 = 0 so you don't have any x's on that side)

- anonymous

Then what?

- anonymous

how do you get the x by itself.. do you get rid of the 5 first or the 6 first?

- anonymous

5x=75-6

- anonymous

Yes... but what is 75-6
5x = 69

- anonymous

but isn't the answer suppose to be x=69/5 and how do you get that?

- anonymous

Yes... divide in you calculator.
13.8

- anonymous

where are you getting 13.8

- anonymous

Once again, I appreciate the help, but I need to see the problem solved from beginning to end. It isn't helping trying to get me to figure out something I don't know. I have to see it work.

- anonymous

would it be 5x-69 x=69÷5 x=69/5

- anonymous

5x=69
x=69÷5
x=69/5

- anonymous

Hello, is anybody there?

- anonymous

I don't appreciate being ignored. Just because I don't understand doesn't mean I should not be helped. If I knew this crap I wouldn't be here in the first place. Thanks for nothing, and I will not recommend this place to anyone.

- anonymous

James, nobody knows that you entered another comment on this page unless they are sitting here watching your post... You need to go and "ask a question" and someone will see it and respond...

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