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Maths Modulus Question: |x-a| + |x+a| = 2a, where a > 0. Watch

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    Hi, I have tried to solve this question for a very long time now, but still cannot get to the solution. I have divided the problem into 3 separate cases of:
    1) x is greater than a.
    2) x is smaller than -a.
    3) x is greater than or equal to -a and smaller than or equal to a.

    But I still can't get anywhere.

    Please could you provide a solution to this question.
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    (Original post by TheMightyBadger)
    Hi, I have tried to solve this question for a very long time now, but still cannot get to the solution. I have divided the problem into 3 separate cases of:
    1) x is greater than a.
    2) x is smaller than -a.
    3) x is greater than or equal to -a and smaller than or equal to a.

    But I still can't get anywhere.

    Please could you provide a solution to this question.
    Can't you remove the modulus-es differently for each according to these separate three cases, and then find solutions for each?
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    (Original post by AHappyStudent)
    Can't you remove the modulus-es differently for each according to these separate three cases, and then find solutions for each?
    I have done that and I got x = a, x = -a and a = a
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    Then for each of these solutions shouldn't you test them against their original bounds to see if each one is valid?

    For x=a, is this valid as the condition on which it is based was x > a ? (I don't think so)

    For x = -a, is this valid as the condition on which it was based was x < -a? (I don't think so)

    For a = a, x can be any value as long as it lies in the range -a <= x <= a ?

    I'm not sure if this solution is correct
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    (Original post by AHappyStudent)
    Then for each of these solutions shouldn't you test them against their original bounds to see if each one is valid?

    For x=a, is this valid as the condition on which it is based was x > a ? (I don't think so)

    For x = -a, is this valid as the condition on which it was based was x < -a? (I don't think so)

    For a = a, x can be any value as long as it lies in the range -a <= x <= a ?

    I'm not sure if this solution is correct
    THANKS! That is the solution in the textbook! This explanation is really clear. Thanks a lot for your help.
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    (Original post by TheMightyBadger)
    THANKS! That is the solution in the textbook! This explanation is really clear. Thanks a lot for your help.
    Ooh, that's quite a nice little solution then. np, happy to help
 
 
 
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