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Math Help - inequality

  1. #1
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    inequality

    ok so i missed a few classes and i have a test comming up soo and i need some help understanding inequalities.

    the example im trying to do is:

    If |x-2|< 2, show that |(x^2+3x+1)/(x+1)| < 7

    form what i could understand from a textbook was something like:

    -2<x-2<2
    0 < x < 4

    and from there on i do a restriction for the x+1 so it cant be divided by 0 right and after that i just kinda get lost... i think i have to find when the top one becomes 0 too but its not exact and i would have to use -b+-sqrt() equation thing soo any help on this one really helps
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  2. #2
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    Quote Originally Posted by sacwchiri View Post
    ok so i missed a few classes and i have a test comming up soo and i need some help understanding inequalities.

    the example im trying to do is:

    If |x-2|< 2, show that |(x^2+3x+1)/(x+1)| < 7

    form what i could understand from a textbook was something like:

    -2<x-2<2
    0 < x < 4

    and from there on i do a restriction for the x+1 so it cant be divided by 0 right and after that i just kinda get lost... i think i have to find when the top one becomes 0 too but its not exact and i would have to use -b+-sqrt() equation thing soo any help on this one really helps
    You need to show that all x in the inequality |x-2|<2 make the other inequality true.

    1)Solve the Bigger Inequality.
    2)Show that solution set of the Smaller is included in the Bigger.
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  3. #3
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    Red face

    Quote Originally Posted by ThePerfectHacker View Post
    You need to show that all x in the inequality |x-2|<2 make the other inequality true.

    1)Solve the Bigger Inequality.
    2)Show that solution set of the Smaller is included in the Bigger.
    ammm that still doesnt tell me much... im kinda slow... could you maybe describe with another example or something like that.. please it would be a great help
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sacwchiri View Post
    ammm that still doesnt tell me much... im kinda slow... could you maybe describe with another example or something like that.. please it would be a great help
    Here's something that might help you.

    If |x-2|< 2, show that |(x^2+3x+1)/(x+1)| < 7

    Suppose |x-2|< 2
    then we have -2 < x - 2 < 2
    => 0 < x < 4
    notice that x = -1 is not included in this solution, so we are in the domain of (x^2+3x+1)/(x+1)

    now, if 0 < x < 4
    then (x^2+3x+1)/(x+1) is at least a little bigger than (0^2+3(0)+1)/((0)+1) = 1
    and (x^2+3x+1)/(x+1) is at most a little smaller than ((4)^2+3(4)+1)/(4+1) = 29/5 = 5.8

    so we see, if |x-2|< 2, then 1 < |(x^2+3x+1)/(x+1)| < 5.8, so in any case |(x^2+3x+1)/(x+1)| < 7
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  5. #5
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    Quote Originally Posted by sacwchiri View Post
    ...
    If |x-2|< 2, show that |(x^2+3x+1)/(x+1)| < 7...
    Hello,

    I'll show you a different attempt to do this problem:
    1. Draw the graph of q(x) = (x + 3x + 1)/(x+1) (blue)
    2. Draw the line y = 7 (red)
    3. Examine the values of q. You'll see that all q(x) < 7 if 0 < x < 4 (green)

    EB
    Attached Thumbnails Attached Thumbnails inequality-unglg_chile.gif  
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  6. #6
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    Quote Originally Posted by earboth View Post
    Hello,

    I'll show you a different attempt to do this problem:
    1. Draw the graph of q(x) = (x + 3x + 1)/(x+1) (blue)
    2. Draw the line y = 7 (red)
    3. Examine the values of q. You'll see that all q(x) < 7 if 0 < x < 4 (green)

    EB
    thanx but i cant realy use graphs for this... but it still helps
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