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Math Help - modulus

  1. #1
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    modulus

    -abs(x+1)+abs(1-x)=2 can anyone tell me how to solve this with a sound approach i dont have any clue what to start with
    abs is mod(modulus)
    answer is x is less than or equal to -1
    Last edited by abdulrehmanshah; February 21st 2014 at 08:32 AM.
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  2. #2
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    Re: modulus

    Quote Originally Posted by abdulrehmanshah View Post
    [INDENT]-abs(x+1)+abs(1-x)=2 can anyone tell me how to solve this with a sound approach i don't have any clue what to start with
    answer is x is less than or equal to -1
    First $|1-x|=|x-1|$ so the problem is $|x-1|-|x+1|=2$.

    We have three regions: $(-\infty,-1],~(-1,1],~\&~[1,\infty)$.

    Is it true for $x=3~?$ NO! So the third region is out.

    Is it true for $x=0~?$ NO! So the second region is out.

    Is it true for $x=-5~?$ So?
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  3. #3
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    Re: modulus

    ok
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  4. #4
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    Re: modulus

    But, of course, if the right-hand side is 1 instead of 2:
    $$
    |x-1|-|x+1|=1
    $$
    then the equation cannot be solved by picking one value from each of the three regions.
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