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Homework Help: Trying to solve |2x-1|-|x+5|-3=0

  1. Jan 11, 2016 #1
    1. The problem statement, all variables and given/known data
    trying to solve |2x-1|-|x+5|-3=0:
    2. Relevant equations
    3. The attempt at a solution

    for x>1/2 I got x=9

    for -5<x<1/2 I got x=-7/3

    but for x<-5 I got -(2x-1)-(-(x+5))-3=0 => x=3 (which is incorrect)

    why x=3 is incorrect , or why I shouldn't considerate the case x<-5 ?
  2. jcsd
  3. Jan 11, 2016 #2


    Staff: Mentor

    Because for that interval, (-∞, -5), you are assuming that x < -5. Therefore x cannot equal +3.
  4. Jan 11, 2016 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    If your assumption of x <= -5 leads to the conclusion that the root is at x = +3 (outside the starting interval), that means that there IS NO ROOT in the interval (-∞,-5). Plot a graph to see why this is so.
  5. Jan 12, 2016 #4


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    Homework Helper
    Education Advisor
    Gold Member

    You should try checking conditions this way although not as efficient of choices:

    2x-1 and x+5 both positive;
    2x-1 and x+5 both negative;
    2x-1 positive and x+5 negative;
    2x-1 negative and x+5 positive.

    Solve the equation in each of the four conditions and check each result.
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