1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Inequality with Modulus Question

  1. Oct 27, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine m :

    [itex]|x-10|<{1}/{m}[/itex]

    if its final form is :

    [itex]|x^{2}+{4}x-140|<1 [/itex]

    2. Relevant equations

    To remove the modulus, square them...

    3. The attempt at a solution

    I have tried to assume that if

    [itex]|x-10|{m}<{1}[/itex]

    then, I can find

    [itex]|x-10|{m}=|x^{2}+{4}x-140|[/itex]

    [itex]|x-10|{m}=|(x+14)(x-10)|[/itex]

    but, can I omit (x-10)?
     
    Last edited: Oct 27, 2012
  2. jcsd
  3. Oct 27, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You can't do that because m might be negative for some x. Try the squaring hint.
    There's an error in that step.
     
  4. Oct 27, 2012 #3
    Okay, sorry it should be

    [itex]|x-10|{m}=|(x+14)(x-10)|[/itex]

    So, if I do this :

    [itex](x-10)^2{m}^2=((x+14)(x-10))^2[/itex]

    is it possible?
     
  5. Oct 27, 2012 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Not quite. Should be [itex]|x-10||m|=|(x+14)(x-10)|[/itex]
    But if you go back to |x−10|<1/m you can observe that m is necessarily non-negative, which simplifies the logic.
    So what form should m take to make that guaranteed, and ensure m non-negative?
     
  6. Oct 28, 2012 #5
    because [itex]|m|=\frac{|(x+14)(x-10)|}{|(x-10)|}[/itex], is it [itex]|m|=|(x+14)|[/itex] ?
     
    Last edited: Oct 28, 2012
  7. Oct 28, 2012 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Almost. If m were negative, would it satisfy the requirements?
     
  8. Oct 28, 2012 #7
    Hmmm... so, I need to add [tex]m>0[/tex] to the equation or something like that.

    [tex]m=|x+14|; m>0[/tex]?
     
  9. Oct 28, 2012 #8

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes, except that you don't now need to specify m >= 0. It follows from m=|x+14|.
     
  10. Oct 29, 2012 #9
    So, the final answer is [tex]m=|x+14|[/tex]?

    I am still in doubt. :confused:
     
  11. Oct 30, 2012 #10

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Looks right to me. Did you try plugging it into the original inequality?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Simple Inequality with Modulus Question
  1. Simple inequalities. (Replies: 4)

  2. Modulus question (Replies: 4)

  3. Modulus Question (Replies: 4)

Loading...