Question

I'm having difficulty with what should be a practice question on two-step equations with fractions. Could someone PLEASE help me understand this?

-4/5x + 2/5 = 1/5

Could someone please show me how to solve this? I know the answer is 1/4 (or at least it should be) but I don't understand how to get there. Please, explain with detail.

Answer 1

First of all @GloryLove : A Warm Welcome to 'Open Study'. Please Read CoC (compulsory to read by all "Open Study" users) : http://openstudy.com/code-of-conduct

Answer 2

Okay, sure.

Answer 3

you have \[\Large -\frac{ 4 }{ 5 }x+\frac{ 2 }{ 5 }=\frac{ 1 }{ 5 }\]

When you have an equation with fractions like this, the first step should be to "clear the fractions" by muliplying both sides of the equation by the LCD. The LCD is easy to see here, since all the fractions have the same den'r of 5. So you need to muliply both sides by 5, being careful to properly distribute that 5 on the left side.

Answer 4

\[\Large 5\cdot \left( \ -\frac{ 4 }{ 5 }x+\frac{ 2 }{ 5 }\right)=\frac{ 1 }{ 5 } \cdot 5\]

Answer 5

\[\Large 5\cdot \left( \ -\frac{ 4 }{ 5 }x\right)+5\cdot \left( \frac{ 2 }{ 5 }\right)=\frac{ 1 }{ 5 } \cdot 5\]

Answer 6

\[\Large \cancel5\cdot \left( \ -\frac{ 4 }{ \cancel5 }x\right)+\cancel5\cdot \left( \frac{ 2 }{ \cancel5 }\right)=\frac{ 1 }{ \cancel5 } \cdot \cancel5\]

Now what do you have?

Answer 7

I'm sorry, I'm confused. So the 5's cancel one another out, right? I'm just lost from there.

Answer 8

Do you understand why the cancel?
they are really just factors of 1.

So when you cancel them, what is left? What does the equation look like?

Answer 9

Here is a different example, with just one term. If I have:

\[\Large2 \cdot \dfrac {7z}{2}\]

Then really, that's:

\[\Large\cancel2 \cdot \dfrac {7z}{\cancel2}=\frac{ \cancel2 }{ \cancel2 }\cdot 7z=1\cdot 7z=7z\]

Answer 10

So do that same kinda thing with each term of your equation.

Answer 11

So.. would it be 1/5 x 5? Because we canceled out the denominators and that's all that's left? I feel like I'm missing something...

Answer 12

I'm not sure I understand your expression there. Is that just the right hand side??

Answer 13

Tell us what you have, for the WHOLE equation, after you multiply both sides by 5 and cancel the den'rs.

Answer 14

I think so.. just on the right side. Math is really not my forte, I guess, I have difficulty making connections between two things, and where to really go from there.

Answer 15

Oh.

Answer 16

I'm really sorry. I appreciate you trying to help me, but I'm just having a hard time understanding. I think I'm going to go ask my dad, maybe I need to see the problem being done in front of me and be guided through it in person. I'm sorry if I wasted your time DebbieG. :/

Answer 17

Don't talk about how you're bad at math. :) When I hear math students do that, I know they are psyching themselves out! :)

Answer 18

Well, it's no waste of time, but if you think that your dad helping will be more effective, then certainly do that. No hard feelings - whatever works for YOU to LEARN is what you should do!! :)

Answer 19

Thank you. I really appreciate the help, though. :)

Answer 20

You're welcome. :)

Answer 21

First of all @GloryLove : A Warm Welcome to 'Open Study'. Please Read CoC (compulsory to read by all "Open Study" users) : http://openstudy.com/code-of-conduct