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Math Help - Absolute Values

  1. #1
    Senior Member
    Joined
    Jul 2008
    Posts
    347

    Absolute Values

    Hi

    For the question:

    Solve for x: abs(x-1) + 3*abs(x+1) ≤ 2

    I've tried to obtain the answer using algebra several times but can't seem to. (The answer is x = -1). Could someone please show me how to do this question?
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  2. #2
    Member
    Joined
    Oct 2006
    Posts
    185
    Thanks
    1
    You can consider different cases to solve this

    |x-1|+3|x+1|\leq 2

    Case 1: x\leq -1

    -(x-1)-3(x+1)\leq 2
    ...
    x\geq -1

    Case 2: -1<x<1

    -(x-1)+3(x+1)\leq 2
    ...
    x\leq -1

    Case 3: x\geq 1

    (x-1)+3(x+1)\leq 2
    ...
    x\leq 0

    Only case 1 gives solution, i.e. x=-1

    Hope this helps!
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