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Math Help - Inequalities

  1. #1
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    Inequalities

    Solve 3 < l X - 5 l .

    When I graph this I can see the answer is 2 < X < 8

    But when I try to sovle it as an inequality it doesn't work. What am I doing wrong?

    3 < X -5

    X > 8

    3 < -x + 5

    X < 2

    Victoria
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  2. #2
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    Quote Originally Posted by Vicky1997 View Post
    Solve 3 < l X - 5 l .

    When I graph this I can see the answer is 2 < X < 8

    But when I try to sovle it as an inequality it doesn't work. What am I doing wrong?

    3 < X -5

    X > 8

    3 < -x + 5

    X < 2

    Victoria
    Hi Victoria,


    Remember this: If |a| > b, then a > b or a < - b.

    So, your algebra is correct. Check your graphing techniques again.

    x - 5 > 3 or x - 5 < -3

    Solving these two inequalities results in x > 8 or x < 2.
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  3. #3
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    Thanks. I see I misread the graph.
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  4. #4
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    So you have 3 < |x-5|
    First of all you must define the module function:
    |x-5|= x-5 , for x-5>=0, meaning for x>=5
    |x-5|= 5-x , for x-5<0, meaning for x<5

    So we go on with the inequality on two sides:
    We take first x>=5. We have 3<x-5 =>x>3+5=>x>8. And because x is supposed to be greater than 5, we have the final partial solution: x>8.

    Next, we have x<5. Our inequality becomes: 3<5-x=>x<5-3=>x<2. Because x<5, the final second partial solution is x<2.

    This is the last result.
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