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Absolute Value Inequality

  1. Oct 9, 2015 #1
    1. 2015-10-10 07.18.11.png

    2. Relevant equations
    Solving Polynomial Inequalities

    3. The attempt at a solution


    2015-10-10 07.18.11.png
    Then I used the property of absolute value inequality to get rid of it.

    But I really don't know if I'm doing the right step. Is this correct? So that I could separate them in two cases and find the solution set.
    2015-10-10 07.39.00.png
     
  2. jcsd
  3. Oct 9, 2015 #2

    andrewkirk

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    Divide it into two alternative cases.
    (1) It's equal to zero. This is the easiest one. What can we say about x in that case?
    (2) It's less than zero. What does that imply about the signs of the numerator and the denominator. Is there any part of either that we can ignore?
     
  4. Oct 9, 2015 #3

    SammyS

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    Hello moondaaay. Welcome to PF !

    Where is the function on the left side of the inequality zero?

    What is its domain?

    upload_2015-10-9_22-8-54.png
     
  5. Oct 11, 2015 #4

    symbolipoint

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    The inequality has four critical values for x, splitting the real number line into five intervals. Each interval can be checked to find which are solutions to the inequality and which are not solutions.
     
  6. Oct 11, 2015 #5
    But what should I do first to remove the absolute value?
     
  7. Oct 11, 2015 #6

    symbolipoint

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    Not really important here. Whatever sign the 3x+7, its absolute value will still be POSITIVE OR ZERO.
     
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