Results 1 to 2 of 2

Math Help - 2 questions on solving inequalities.

  1. #1
    Member Mathelogician's Avatar
    Joined
    Jun 2010
    From
    Iran
    Posts
    89
    Thanks
    1

    2 questions on solving absolute value inequalities.

    Hi all,

    Thanks.
    Last edited by Mathelogician; June 22nd 2010 at 11:47 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    With your first solution, the problem is that in your logic, you have introduced spurious solutions. Just try plugging in a few numbers here and there in your final domain, and you'll see that there are numbers in your final answer that do not satisfy the initial inequality. What your logic has done is essentially take each individual absolute value sign and get a domain for each of those. Then you take the intersection of those two domains. What you have shown is that the actual domain must be a subset of (-8,9). But you can easily see that -8 doesn't work, and should therefore not be part of the solution. One suggestion might be to think of this problem as follows: x's distance from 3 added to its distance from -2 must be less than 11.

    In problem 2, your logic is rather mixed up. Regions 4 and 5, if taken together as both true, can imply anything, because they are mutually exclusive! You can't be in both of those regimes simultaneously. Finally, I'm not sure I agree with your overall approach. All of these cases are "or"-ed together. That is, you're in case 1 or case 2 or... But you're trying to get conditions that are true regardless of which case you're in. In logic, to accomplish that, you would have to show that, no matter which case you're in (and assuming you've done this for all cases), you get the same result every time. But you're coming up with different results for each case. It is logically impermissible, then, to claim that all of the conditions are always true, when they need not necessarily hold in every single case. If I were you, I'd use some different sort of strategy. Honestly, I'd just try poking numbers into the inequality, start seeing a pattern, and then see if you can prove that pattern.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problems solving some inequalities questions
    Posted in the Algebra Forum
    Replies: 9
    Last Post: March 29th 2011, 02:39 PM
  2. A few questions about INEQUALITIES
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 9th 2009, 02:25 AM
  3. i have two questions about inequalities
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 22nd 2009, 01:05 PM
  4. Solving inequalities
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 5th 2008, 11:14 PM
  5. Solving Inequalities
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 11th 2008, 01:01 PM

Search Tags


/mathhelpforum @mathhelpforum