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Math Help - Inequality problems

  1. #1
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    Inequality problems

    I have a question on what I did wrong
    The first problem:
    1. was to solve the inequality x^2+6x-27<0. The solution is x is in the open interval (A, B) where A is:___ and B is:___
    for that i did (x-9)(x+3) so i thought the answer for A would have been 9 or (9,infinity) but it says it was wrong, and for be either -3 or (-infinity,-3)
    2. was to write the answer in interval notation for (x-5)(x-11)>0 I got (5,infinity)U(11,infinity) webwork said it is incorrect too, so can anyone help me out what mistake i made for those two problems?
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  2. #2
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    Miami, FL
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    Quote Originally Posted by Girlaaaaaaaa View Post
    I have a question on what I did wrong
    The first problem:
    1. was to solve the inequality x^2+6x-27<0. The solution is x is in the open interval (A, B) where A is:___ and B is:___
    for that i did (x-9)(x+3) so i thought the answer for A would have been 9 or (9,infinity) but it says it was wrong, and for be either -3 or (-infinity,-3)
    2. was to write the answer in interval notation for (x-5)(x-11)>0 I got (5,infinity)U(11,infinity) webwork said it is incorrect too, so can anyone help me out what mistake i made for those two problems?
    On the first question, it's (x+9)(x-3). Also, the answer of the inequality (x-A)(x-B)<0 is (let's say A<B) the open interval (A,B), instead of the inequality (x-A)(x-B)>0, where the answer is (-oo,A)U(B,+oo).
    This happens because if we want (x-A)(x-B)>0, both of the parenthesis have to be positive, or both negative. Thus, must be (x-A>0 and x-B>0) OR (x-A<0 and x-B<0). Therefore, (x>A and x>B) OR (x<A and x<B). So, if A<B, the first parenthesis gives x>B and the second x<A, which, in a diferent form are (B, +oo) and (-oo, A) corespondingly.

    Hence, the inequality (x-A)(x-B)<0 gives the opposite answer, which (A, B).
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