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

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2. 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

3. anonymous

Im sorry ; ~;

4. UnkleRhaukus

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

5. UnkleRhaukus

the first term simplifies . . .

5x^2 + 1/x <1?

7. UnkleRhaukus

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

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

9. UnkleRhaukus

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

10. UnkleRhaukus

*from

1/x < -4

12. UnkleRhaukus

yes

13. UnkleRhaukus

now if we multiply both sides by x . . .

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

15. 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)

16. 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

17. UnkleRhaukus

hmmm,

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

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20. UnkleRhaukus

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

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

22. UnkleRhaukus

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

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

24. UnkleRhaukus

oh, ok

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

26. UnkleRhaukus

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

27. 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

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?

29. UnkleRhaukus

that works!

|dw:1435671952655:dw| Next question, if you have time

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32. Loser66

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

33. Loser66

got it?

Yeah but it's =<

35. Loser66

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