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Exponential inequations.

  1. Oct 2, 2008 #1
    1. The problem statement, all variables and given/known data
    1) 5x+4-5x-1<24
    2) 2x+2-1>=22x+3
    3) 21-x-2x+1/2x-1<0

    2. Relevant equations
    At the 2nd I do like this:
    2x+2-22x>=4 devide by 2
    2x+1-22x-1>=2
    x+1-2x+1>=1
    -x>=-1 devide by (-1)
    x=<1
    but when i put 0 in x the inequation is incorrect, what I have mistake, please tell me.
    If you can halp me in anothers inequations, thanks a lot.

    3. The attempt at a solution
     
  2. jcsd
  3. Oct 2, 2008 #2
    Please can you help for this?
     
  4. Oct 2, 2008 #3
    I need the help urgently, please help!
     
  5. Oct 2, 2008 #4

    statdad

    User Avatar
    Homework Helper

    Your simplifications with the exponents aren't correct. Try this:

    [tex]
    \begin{align*}
    2^{x+2} - 2^{2x} & \ge 4\\
    2^x \cdot 2^2 - 2^{2x} & \ge 4\\
    4\cdot 2^x - 2^{2x} -4 & \ge 0\\
    2^{2x} - 4\cdot 2^x + 4 & \le 0
    \end{align*}
    [/tex]

    Now, for ease of reading, let

    [tex]
    u = 2^x \Rightarrow u^2 = 2^{2x}
    [/tex]

    so the inequality is now

    [tex]
    u^2 - 4u + 4 & \le 0
    [/tex]
     
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