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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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  1. sloppycanada
    • one year ago
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    |dw:1435669658962:dw|

  2. anonymous
    • one year ago
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    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
    • one year ago
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    Im sorry ; ~;

  4. UnkleRhaukus
    • one year ago
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    \[\frac{5x+1}{x}<1\\ \frac{5x}x+\frac1x<1\\ \quad\dots\quad<1\]

  5. UnkleRhaukus
    • one year ago
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    the first term simplifies . . .

  6. sloppycanada
    • one year ago
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    5x^2 + 1/x <1?

  7. UnkleRhaukus
    • one year ago
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    not quite, the x's in the first term dont multiply, they cancel

  8. sloppycanada
    • one year ago
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    Oh. Okay so 5 + 1/x <1?

  9. UnkleRhaukus
    • one year ago
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    good, now the next step is to take away 5 form both sides

  10. UnkleRhaukus
    • one year ago
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    *from

  11. sloppycanada
    • one year ago
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    1/x < -4

  12. UnkleRhaukus
    • one year ago
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    yes

  13. UnkleRhaukus
    • one year ago
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    now if we multiply both sides by x . . .

  14. sloppycanada
    • one year ago
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    1 = -4x So x = -1/4

  15. UnkleRhaukus
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    hmmm,

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

  19. sloppycanada
    • one year ago
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    |dw:1435671020481:dw|

  20. UnkleRhaukus
    • one year ago
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    im not sure what our final answer should be for the first one

  21. sloppycanada
    • one year ago
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    If we used -1/4 as our answer, I get the 1 on my calculator.

  22. UnkleRhaukus
    • one year ago
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    but is x less or greater? than -1/4

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

  24. UnkleRhaukus
    • one year ago
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    oh, ok

  25. sloppycanada
    • one year ago
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    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
    • one year ago
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    x < -1/4 says all values of x that are less than -1/4

  27. Loser66
    • one year ago
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    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

  28. sloppycanada
    • one year ago
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    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
    • one year ago
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    that works!

  30. sloppycanada
    • one year ago
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    |dw:1435671952655:dw| Next question, if you have time

  31. sloppycanada
    • one year ago
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    |dw:1435672689916:dw|

  32. Loser66
    • one year ago
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    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
    • one year ago
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    got it?

  34. sloppycanada
    • one year ago
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    Yeah but it's =<

  35. Loser66
    • one year ago
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    |dw:1435673140046:dw| for this, not for the last one

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