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Math Help - Inequality Help.

  1. #1
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    Question Inequality Help.

    [These are FRACTIONS. The Slash signs are for FRACTIONS]

    1/6x + 1/2 < 1/12x + 2/3

    There are four choices to what this could be.

    a: x < 14/3
    b: x > 14/3
    c: x < 2
    d. x > 2

    --------------------------------------------------------------------

    -4 (3x - 6) < 3 (x + 3)

    There are four choices to this also.

    a. x < -1
    b. x > 1
    c. x < 1
    d. x > -1

    --------------------------------------------------------------------

    3 |2x - 4| - 5 < 7

    There are four choices to this.

    a. 0 < x < 4
    b. x < - 4 or x > 0
    c. - 4 < x < 0
    d. x < 0 or x > 4

    --------------------------------------------------------------------

    |x + 1| - 2 > 5

    There are four choices.

    a. 6 < x < -8
    b. x > 8 or x < -6
    c. 8 < x < -6
    d. x > 6 or x < -6

    -------------------------------------------------------------------

    Dave's grades on four tests were 95, 76, 82, 65. What must his lowest grade on the next test be to have an average greater than 80.

    -------------------------------------------------------------------

    Six less than a number is between (-3) and 11. What real numbers are possible soulutions ?

    -------------------------------------------------------------------

    Thank you for your help !!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by omgitzbella View Post
    [These are FRACTIONS. The Slash signs are for FRACTIONS]

    1/6x + 1/2 < 1/12x + 2/3

    There are four choices to what this could be.

    a: x < 14/3
    b: x > 14/3
    c: x < 2
    d. x > 2
    Do you mean:

    \frac{1}{6x} + \frac{1}{2} < \frac{1}{12x} + \frac{2}{3}

    or

    \frac{1}{6}~x + \frac{1}{2} < \frac{1}{12}~x + \frac{2}{3} ?

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by omgitzbella;83389--------------------------------------------------------------------

    [tex
    -4 (3x - 6) < 3 (x + 3)[/tex]

    There are four choices to this also.

    a. x < -1
    b. x > 1
    c. x < 1
    d. x > -1
    -4 (3x - 6) < 3 (x + 3)

    expand brackets:

    -12x + 24 < 3 x + 9

    add 12x to both sides:

    24 < 15 x + 9

    Now subtract 9 from both sides:

    15 < 15 x

    and divide by 15, to get?

    RonL
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    i meant the second suggestion that you posted. Where x isn't included in the fraction.
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  5. #5
    MHF Contributor red_dog's Avatar
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    Quote Originally Posted by omgitzbella View Post

    3 |2x - 4| - 5 < 7

    There are four choices to this.

    a. 0 < x < 4
    b. x < - 4 or x > 0
    c. - 4 < x < 0
    d. x < 0 or x > 4
    3\cdot |2x-4|-5<7\Leftrightarrow 3\cdot |2x-4|<12\Leftrightarrow
    \Leftrightarrow|2x-4|<4\Leftrightarrow -4<2x-4<4\Leftrightarrow 0<2x<8\Leftrightarrow 0<x<4
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  6. #6
    MHF Contributor red_dog's Avatar
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    Quote Originally Posted by omgitzbella View Post
    |x + 1| - 2 > 5

    There are four choices.

    a. 6 < x < -8
    b. x > 8 or x < -6
    c. 8 < x < -6
    d. x > 6 or x < -6
    |x+1|-2>5\Leftrightarrow |x+1|>7\Leftrightarrow x+1<-7 \ \text{or} \ x+1>7\Leftrightarrow x<-8 \ \text{or} \ x>6
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  7. #7
    Bar0n janvdl's Avatar
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    Quote Originally Posted by omgitzbella View Post
    [These are FRACTIONS. The Slash signs are for FRACTIONS]
    I believe we get the general idea
    -------------------------------------------------------------------

    Dave's grades on four tests were 95, 76, 82, 65. What must his lowest grade on the next test be to have an average greater than 80.
    \frac{95 + 76 + 82 + 65 + x}{5} > 80 (Remember there will be 5 tests...)

    = 95 + 76 + 82 + 65 + x > 400

    = 318 + x > 400

    = x > 82
    -------------------------------------------------------------------

    Six less than a number is between (-3) and 11. What real numbers are possible soulutions ?
    -3 < x - 6 < 11 (Get rid of the -6 by adding six to the left and right side)

    = 3 < x < 17

    -------------------------------------------------------------------

    Thank you for your help !!!
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  8. #8
    MHF Contributor red_dog's Avatar
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    Quote Originally Posted by omgitzbella View Post
    Dave's grades on four tests were 95, 76, 82, 65. What must his lowest grade on the next test be to have an average greater than 80.

    -------------------------------------------------------------------

    Six less than a number is between (-3) and 11. What real numbers are possible soulutions ?

    -------------------------------------------------------------------

    Thank you for your help !!!
    \displaystyle\frac{95+76+82+65+x}{5}>80\Leftrighta  rrow 318+x>400\Leftrightarrow x>82


    -3<x-6<11\Rightarrow 3<x<17
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