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Math Help - Inequalities

  1. #1
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    Inequalities

    How to solve this inequality

    1) -3x^3 >= 81

    and which of the following inequalities has a solution

    2) x-3<3-x<x-5 or x-3>3-x>x-5
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  2. #2
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    Re: Inequalities

    Quote Originally Posted by darkangel06 View Post
    How to solve this inequality

    1) -3x^3 \ge 81

    and which of the following inequalities has a solution

    2)  x-3<3-x<x-5 \text{ or } x-3>3-x>x-5
    -3x^3 \ge 81 is equivalent to
    \\3x^3 \le -81\\x^3\le -27\\x^3\le -3^3
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  3. #3
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    Re: Inequalities

    Quote Originally Posted by darkangel06 View Post
    How to solve this inequality

    1) -3x^3 >= 81
    What Plato said! And the fact that x^3 is an increasing function.

    and which of the following inequalities has a solution

    2) x-3<3-x<x-5 or x-3>3-x>x-5
    x- 3< x- 5 is the same as -3< -5 which is not true.

    x- 3> x- 5 is the same as -3> -5 which is true.
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  4. #4
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    Re: Inequalities

    Quote Originally Posted by darkangel06 View Post
    How to solve this inequality

    1) -3x^3 >= 81

    and which of the following inequalities has a solution

    2) x-3<3-x<x-5 or x-3>3-x>x-5
    detailed solution below
    Last edited by votan; October 4th 2013 at 07:03 AM.
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  5. #5
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    Re: Inequalities

    for the second one It just says to explain which one equality has a solution.
    and in the answers the second inequality has a solution but i really dont know how :/
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  6. #6
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    Re: Inequalities

    Quote Originally Posted by darkangel06 View Post
    for the second one It just says to explain which one equality has a solution.
    and in the answers the second inequality has a solution but i really dont know how :/
    first: x - 3 < 3 - x < x - 5
    x < 3 OR x > 4 (OR condition if the double inequality were two separate inequalties) no AND solution

    *******3......4******** (* means solultion)

    second: x - 3 > 3 - x > x - 5
    x > 3 AND x < 4 (AND condition)

    .........3*******4.........
    Last edited by votan; October 4th 2013 at 07:01 AM.
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  7. #7
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    Re: Inequalities

    Ok so how did you get x>3 and x< 4 in the second equation
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  8. #8
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    Re: Inequalities

    Quote Originally Posted by darkangel06 View Post
    Ok so how did you get x>3 and x< 4 in the second equation
    x - 3 > 3 - x > x - 5

    Split this into two inequalities:
    x - 3 > 3 - x ==> x + x > 3 + 3 ==> 2x > 6 ==> x > 6/2 = 3 (group all x's on one side and the numbers on the other side)
    3 - x > x - 5 == 3 + 5 > x + x ==> 8 > 2x ==> (8/2) > x or x < 4 by reading the inequality from right to left.
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