Five rational function equations to help me with, if you'd be oh so kind.
(5x+1)/x < 1

- sloppycanada

Five rational function equations to help me with, if you'd be oh so kind.
(5x+1)/x < 1

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- katieb

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- sloppycanada

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- anonymous

Ok i have an idea but i might be wrong so hopefully this might help.
https://www.khanacademy.org/math/algebra2/rational-expressions/solving-rational-equations/v/solving-rational-equations-2

- anonymous

Im sorry ; ~;

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## More answers

- UnkleRhaukus

\[\frac{5x+1}{x}<1\\
\frac{5x}x+\frac1x<1\\
\quad\dots\quad<1\]

- UnkleRhaukus

the first term simplifies . . .

- sloppycanada

5x^2 + 1/x <1?

- UnkleRhaukus

not quite, the x's in the first term dont multiply, they cancel

- sloppycanada

Oh. Okay so 5 + 1/x <1?

- UnkleRhaukus

good, now the next step is to take away 5 form both sides

- UnkleRhaukus

*from

- sloppycanada

1/x < -4

- UnkleRhaukus

yes

- UnkleRhaukus

now if we multiply both sides by x . . .

- sloppycanada

1 = -4x
So x = -1/4

- UnkleRhaukus

we get
-1/4 < x
but this is because we assumed that x was not negative
(we didn't swap the direction of inequality)

- UnkleRhaukus

if we had assumed that x was negative, we would have switched the direction of inequality, when we multiplied both sides by x,
we would have gotten
-1/4 > x

- UnkleRhaukus

hmmm,

- sloppycanada

Okay thanks. For this next one (assuming we're good here), wouldn't I just want to find the quadratic parts?

- sloppycanada

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- UnkleRhaukus

im not sure what our final answer should be for the first one

- sloppycanada

If we used -1/4 as our answer, I get the 1 on my calculator.

- UnkleRhaukus

but is x less or greater? than -1/4

- sloppycanada

According to the original problem, the answer (once you plug in the value for x) should be less than one.

- UnkleRhaukus

oh, ok

- sloppycanada

So for the first question, I think the answer would just be -1/4 < x
Which would mean anything smaller than -1/4 right?

- UnkleRhaukus

x < -1/4
says all values of x that are less than -1/4

- Loser66

If \(\dfrac{a}{b}<1\) , that is b>a
hence, in your case, x > 5x+1
that gives us \(x<-\dfrac{1}{4}\). Dat sit

- sloppycanada

So I think that would be right... let me plug in -1/5.. that equals "0" which means x < -1/4 as our final answer right?

- UnkleRhaukus

that works!

- sloppycanada

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Next question, if you have time

- sloppycanada

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- Loser66

a/b <0 iff a, b are different sign. That is if a >0, then b <0 and vice versa
solve for them.

- Loser66

got it?

- sloppycanada

Yeah but it's =<

- Loser66

|dw:1435673140046:dw| for this, not for the last one

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