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Soling an inequality using Algebraic method

  1. Mar 13, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve
    |3x-7|-|x-8|>4



    3. The attempt at a solution

    so i made columns... and using the columns i made a number line..

    7/3 on the left as a point, with a column on its left, and 8 with a column on its right and sharing a coumn in the middle with 7/3

    so i have..

    |3x-7| => (3x-7), X>OREQUAL 7/3
    -(3x-7) x<7/3


    |x-8| => (x-8) x>or equal 8
    -(x-8) x< 8

    * i algebraeicly solved 3 different inequalities after this
    1. -(3x-7)-[-(x-8)]>4 (this was not crossed out)-- the answer was crossed x<-2
    2. -(3x-7) - (x-8)>4 (this WAS CROSSED OUT)
    3. (3x-7) - (x-8) >4 (this was not crossed out) - the answered was crossed x>2/3

    i understand i am supposed to compare the three inequalities after to get the answer, but i dont understand the thinking of how to go about the questoin in terms of CREATING the THREE inequalities..

    So how exactly do i... evaluate the different possibilites can some one give me something to run with or think about, so i can solve this :(
     
  2. jcsd
  3. Mar 13, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Unfortunately, you left out the crucial part- HOW you got "-2" as the answer. Distributing the "-"s, -3x+ 7+ x- 8= -2x- 1> 4. Can you solve that?

    Again, you haven't shown how you got that. "x> 2/3" is wrong. Where did that "3" in the denominator come from?

     
  4. Mar 14, 2012 #3
    Unfortunately, you left out the crucial part- HOW you got "-2" as the answer. Distributing the "-"s, -3x+ 7+ x- 8= -2x- 1> 4. Can you solve that?

    - -2x -1 >4
    x < -5/3

    lol so basically i rushed and made smoe stupid simple agebraeic errors... Uhh i feel really embarassed i didn't look more carefully at this before i posted.... x.x
     
  5. Mar 14, 2012 #4
     
    Last edited by a moderator: May 5, 2017
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