Question

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

Answer 1

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

Answer 2

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.

Answer 3

a)

Answer 4

the x is not below the 4

Answer 5

oh, good. That's even better.

Answer 6

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

Answer 7

Right?

Answer 8

Yes

Answer 9

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?

Answer 10

-x/3

Answer 11

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

Answer 12

-1x/3

Answer 13

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

Answer 14

yes

Answer 15

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

a*1 = a

Answer 16

right

Answer 17

so then:

\[a = 1*a = \frac{3}{3}*a = \frac{3a}{3} = a\]

Answer 18

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

Answer 19

yes

Answer 20

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

Answer 21

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.

Answer 22

don't know

Answer 23

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.

Answer 24

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

Answer 25

-3x/3

Answer 26

Right.

Answer 27

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:

\[\frac{5}{1}\]

Answer 28

5/1+2/5

Answer 29

Ok, we have this (after changing the denominator on -x)

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

Answer 30

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

Answer 31

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.

Answer 32

Hello

Answer 33

One second.

Answer 34

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

Answer 35

James are you there?

Answer 36

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

Answer 37

Because you have denominators and an = sign, you need to find a common denominator.

What is the common denominator using 5 and 3

Answer 38

15

Answer 39

So multiply the whole equation by 15.

Answer 40

Yes.. every term.

Answer 41

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

Answer 42

Yep. And distribute.

Answer 43

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

Answer 44

Cancel out the denominators into the numerators.

Answer 45

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

Answer 46

-15x + 6 = 75 - 20x

Answer 47

Now solve for x in the usual way.

Answer 48

Blexting, let him do it.

Answer 49

I don't know

Answer 50

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

Answer 51

-20x

Answer 52

so add 20x to both sides

Answer 53

James, if you have an equation:

5x + 4 = 4

How do you solve for x?

Answer 54

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

Answer 55

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

Answer 56

THE LAST ONE should be a plus sign

Answer 57

Good so add like terms.

Answer 58

-5x+6=75-x

Answer 59

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

Answer 60

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

Answer 61

5

Answer 62

So you have

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

Answer 63

Then what?

Answer 64

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

Answer 65

5x=75-6

Answer 66

Yes... but what is 75-6

5x = 69

Answer 67

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

Answer 68

Yes... divide in you calculator.

13.8

Answer 69

where are you getting 13.8

Answer 70

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.

Answer 71

would it be 5x-69 x=69÷5 x=69/5

Answer 72

5x=69
x=69÷5
x=69/5

Answer 73

Hello, is anybody there?

Answer 74

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.

Answer 75

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...