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How to solve inequality

  1. Oct 16, 2012 #1
    1. The problem statement, all variables and given/known data
    [tex]\sqrt[4]{2x + 1} - 0.1 < \frac{1}{2}x + 1 < \sqrt[4]{2x + 1} + 0.1[/tex]


    2. Relevant equations



    3. The attempt at a solution

    I'm having trouble getting just an 'x' by itself in the middle because of the 4th root. How should I solve this inequality? I tried everything but always end up with something to the 4th power after expanding 4 binomials.

    (Solution: -0.368935 < x < 0.677669)
     
  2. jcsd
  3. Oct 16, 2012 #2

    LCKurtz

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    I would think about expanding ##\sqrt[4]{1+2x}## as a binomial or Taylor series with error estimates.
     
  4. Oct 17, 2012 #3

    ehild

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    Try to solve the inequalities separately.

    [tex]\sqrt[4]{2x + 1} < \frac{1}{2}x + 1.1 [/tex]
    [tex]\sqrt[4]{2x + 1} > \frac{1}{2}x + 0.9 [/tex]

    ehild
     
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