anonymous
  • anonymous
I need some help understanding clearing fractions. Example: -x+2/5=5-4/3x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
-x+2/5=5-4/3x
anonymous
  • 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
  • anonymous
a)

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anonymous
  • anonymous
the x is not below the 4
anonymous
  • anonymous
oh, good. That's even better.
anonymous
  • anonymous
\[-x + \frac{2}{5} = 5 - \frac{4}{3}x\]
anonymous
  • anonymous
Right?
anonymous
  • anonymous
Yes
anonymous
  • 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
  • anonymous
-x/3
anonymous
  • anonymous
Nearly, but it must maintain equivalence. 3/3 is 1 right?
anonymous
  • anonymous
-1x/3
anonymous
  • anonymous
No. Stop guessing and listen. 3/3 = 1. Right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Ok, and 1 times any number gives you the same number right? a*1 = a
anonymous
  • anonymous
right
anonymous
  • anonymous
so then: \[a = 1*a = \frac{3}{3}*a = \frac{3a}{3} = a\]
anonymous
  • anonymous
Did you follow that? Sometimes it's hard to read on one line.
anonymous
  • anonymous
yes
anonymous
  • anonymous
Ok, so what is -x as a multiple of 1/3?
anonymous
  • 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
  • anonymous
don't know
anonymous
  • 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
  • anonymous
\[\frac{-3x}{3} = -x\] Right?
anonymous
  • anonymous
-3x/3
anonymous
  • anonymous
Right.
anonymous
  • 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
  • anonymous
5/1+2/5
anonymous
  • anonymous
Ok, we have this (after changing the denominator on -x) \[\frac{-3x}{3} + \frac{2}{5} = 5 -\frac{4x}{3}\]
anonymous
  • 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
  • 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
  • anonymous
Hello
anonymous
  • anonymous
One second.
anonymous
  • anonymous
Starting from \[\frac{-3x}{3} + \frac{2}{5} = 5 - \frac{4x}{3}\] Can you solve for x?
anonymous
  • anonymous
James are you there?
anonymous
  • anonymous
-x+2/5=5-4x/3
anonymous
  • 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
  • anonymous
15
anonymous
  • anonymous
So multiply the whole equation by 15.
anonymous
  • anonymous
Yes.. every term.
anonymous
  • anonymous
15(-x+2/5)=15(5-4/3x)
anonymous
  • anonymous
Yep. And distribute.
anonymous
  • anonymous
(15)(-x) + (15)(2) (15)(5) - (15)(4x) ----- = ------- 5 3
anonymous
  • anonymous
Cancel out the denominators into the numerators.
anonymous
  • anonymous
(15)(-x) + (3)(2) = (15)(5) - 5(4x)
anonymous
  • anonymous
-15x + 6 = 75 - 20x
anonymous
  • anonymous
Now solve for x in the usual way.
anonymous
  • anonymous
Blexting, let him do it.
anonymous
  • anonymous
I don't know
anonymous
  • 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
  • anonymous
-20x
anonymous
  • anonymous
so add 20x to both sides
anonymous
  • anonymous
James, if you have an equation: 5x + 4 = 4 How do you solve for x?
anonymous
  • anonymous
What do you get James when you +20x to both sides?
anonymous
  • anonymous
20x-15x+6=75-20x=20X
anonymous
  • anonymous
THE LAST ONE should be a plus sign
anonymous
  • anonymous
Good so add like terms.
anonymous
  • anonymous
-5x+6=75-x
anonymous
  • anonymous
20x - 15x (20 - 15 = ?)
anonymous
  • anonymous
-20x + 20x = (-20 + 20 = ?)
anonymous
  • anonymous
5
anonymous
  • anonymous
So you have 5x + 6 = 75 (because your -20 + 20 = 0 so you don't have any x's on that side)
anonymous
  • anonymous
Then what?
anonymous
  • anonymous
how do you get the x by itself.. do you get rid of the 5 first or the 6 first?
anonymous
  • anonymous
5x=75-6
anonymous
  • anonymous
Yes... but what is 75-6 5x = 69
anonymous
  • anonymous
but isn't the answer suppose to be x=69/5 and how do you get that?
anonymous
  • anonymous
Yes... divide in you calculator. 13.8
anonymous
  • anonymous
where are you getting 13.8
anonymous
  • 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
  • anonymous
would it be 5x-69 x=69÷5 x=69/5
anonymous
  • anonymous
5x=69 x=69÷5 x=69/5
anonymous
  • anonymous
Hello, is anybody there?
anonymous
  • 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
  • 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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