1/x - 4/3x = 1/5: I don't get why this doesn't work

[torrobinson]

edit: whoops, move to "beginner algebra" please!

Ok. I just KNOW this will be another stupid mistake that I don't see now, and I'll feel like an idiot when I realize how simple it was. But:

1/x - 4/3x = 1/5

greatest common denominator is 15x, right?

15(1/x) - 5(4/3x) = 3x(1/5)

is

15/15x - 20/15x = 3x/15x

cross out the common denominator and:

15 - 20 = 3x

-5 = 3x

x= -5/3
------------

But when I graph to check this, I'm totally off..... yeah.... :S


edit: sorry if this is in the wrong forum-section. This is where I bookmarked the page earlier.... this question is probably considered beginner algebra. It was a small question on the start of an exam I had today, and when I talked to another classmate, we both got the same answer of -5/3

 

[Mrspi]

Re: I don't get why this doesn't work.

Ok. I just KNOW this will be another stupid mistake that I don't see now, and I'll feel like an idiot when I realize how simple it was. But:

1/x - 4/3x = 1/5

greatest common denominator is 15x, right?

15(1/x) - 5(4/3x) = 3x(1/5)

is

15/15x - 20/15x = 3x/15x

cross out the common denominator and:

15 - 20 = 3x

-5 = 3x

x= -5/3
------------

But when I graph to check this, I'm totally off..... yeah.... :S


edit: sorry if this is in the wrong forum-section. This is where I bookmarked the page earlier.... this question is probably considered beginner algebra. It was a small question on the start of an exam I had today, and when I talked to another classmate, we both got the same answer of -5/3

I'm not sure what you mean that you are "totally off when I graph this."

Substitute (-5/3) for x in the original equation:

1 / (-5/3) - 4 / 3(-5/3) = 1/5

1*(-3/5) - 4*(-3/15) = ? 1/5

-3/5 + 12/15 =? 1/5

-9/15 + 12/15 =? 1/5

3/15 = 1/5

It checks...I don't see where the difficulty is.

 

[torrobinson]

Good thing I left my answer as that!

Maybe I'm misunderstanding something.... if I graph y= 1/x - 4/3x and y= 1/5 , the solutions are where they intersect, right?

 

[Mrspi]

Good thing I left my answer as that!

Maybe I'm misunderstanding something.... if I graph y= 1/x - 4/3x and y= 1/5 , the solutions are where they intersect, right?

Yep...and my graphs of

y = 1 / x - 4 / (3x)
and
y = 1/5

DO intersect at x = -5/3

Be sure you have entered the two equations correctly....you will probably need some parentheses.

1/3 x and 1 / (3x) are NOT interpreted the same way by your calculator!

 

[torrobinson]

Good thing I left my answer as that!

Maybe I'm misunderstanding something.... if I graph y= 1/x - 4/3x and y= 1/5 , the solutions are where they intersect, right?

Yep...and my graphs of

y = 1 / x - 4 / (3x)
and
y = 1/5

DO intersect at x = -5/3

Be sure you have entered the two equations correctly....you will probably need some parentheses.

1/3 x and 1 / (3x) are NOT interpreted the same way by your calculator!

I had this entered!:
Y1=(1/x)-(4/3x)

I never knew it made that much of a difference. My teacher is always reminding people to use brackets around denominators with more than one term, but I never even knew.... thanks.

(I guess 4/3x is the same as x(4/3), then?