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Math Help - modulus equation

  1. #1
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    modulus equation

    i have the equation \mid x - 1 \mid  = 1 - x
    i opened up the modulus to get x - 1 = 1 - x & 1 - x = 1 - x

    and the answer is supposed to be the inequality x \le 1 but ive no clue how to get to this.
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  2. #2
    MHF Contributor red_dog's Avatar
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    First of all, the right member must be nonnegative, as the left member is.

    That means 1-x\geq 0\Rightarrow x\leq 1.

    In this case the equation is 1-x=1-x which is true for all x\leq 1
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  3. #3
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    Quote Originally Posted by renlok View Post
    i have the equation \mid x - 1 \mid  = 1 - x
    i opened up the modulus to get x - 1 = 1 - x
    Provided x-1\ge 0.
    x- 1= 1- x reduces to 2x= 2 and then x= 1. Yes, that is satisifies x- 1= 0 and so is a valid solution.

    & 1 - x = 1 - x
    Provided x- 1< 0.
    1-x= 1- x reduces to 0= 0 which is true for all x but we still have "x- 1< 0". Every x such that x- 1< 0, which says x< 1, is a solution. Putting that together with the first case says that all x such that x\le 1 is a solution.

    and the answer is supposed to be the inequality x \le 1 but ive no clue how to get to this.
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