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Math Help - sqrt(x + 5) - sqrt(8 - x) < 1: Need help to find my mistake

  1. #1
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    sqrt(x + 5) - sqrt(8 - x) < 1: Need help to find my mistake

    hi guys,

    can anyone help me to find my mistake, I can't figure out what's wrong, probably something small.

    the correct answer should be -5<=x<=4

    I got -1<=x<=4

    cheers !
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  2. #2
    MHF Contributor

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    It's not so much a matter of a single "mistake" as that your whole concept is wrong! Do you understand that if x< y it does not necessarily follow that x^2< y^2? -3< 2 but 9 is NOT less than 4.

    I would do this instead: solve the equation \sqrt{x+ 5}- \sqrt{8- x}= 1. Those points separate "<" and ">". Check one point in each interval to see if the the inequality is satisfied in that interval.
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