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    Determine in terms of an inequalities

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    Inequality Calculations. See attached file for full problem description.

    9.1 52.
    [8x - 3(3x + 2)] - 5 ≥ 3(x + 4) - 2x

    First distribute it into the parenthesis, then move x into the left side of the inequality. Remember to change the sign if a negative number is multiplied or divided.

    72. Elaine's height is 67 in. Determine, in terms of an inequality, those weights W that will keep her body mass index below 25.
    The body mass index is defined as

    Her height is 67 inches, and BMI <25

    Her weight has to be less than 159.64 pounds.

    76. A long-distance telephone call using Down East Calling costs 10 cents for the first minute and 8 cents for each additional minute. The same call, placed on Long Call Systems, cost 16 cents for the first minute and 6 cents for each additional minute. For what length phone calls is Down East Calling less expensive?
    Assume x minutes
    The cost of long-distance call is 10 + 8(x-1)
    The cost for Long call system is 16 + 6(x-1)
    It is obvious x>0
    So

    So less than 6.5 minutes, Down east calling is less expensive.

    80. Bayside Insurance offers two plans. Under plan A, Giselle would pay the first $50 of her medical bills and 20% of all bills after that. Under plan B, Giselle would pay the first $250 of bills, but only 10% of the rest. For what amount of medical bills will plan B save Giselle money? Assume that her bills will exceed $250.
    Assume the medical bills is x dollars.
    Then plan A: 50 + 20%(x-50) = 0.2x + 40
    Place B: 250 + 10%(x-250) = 0.1x + 225
    For plan B to save money, it satisfy

    When the bill is over $1850, she pays less with plan B.
    9.2
    66. Young's rule for determining the amount of a medicine dosage for a child is given by

    C = where a is the childs age and d is the usual adult dosage, in milligrams

    The dosage of a medication for a 5 year old child must stay between 50mg and 100 mg. Find the equivalent adult dosage.
    A= 5

    So the adult dosage is between 170 mg and 340 mg.
    9.3
    36. |9y - 2| = 17

    52. 2|2x - 7| + 11 = 25
    When , , the equation can be simplified as

    When , the equation is

    So the solution is x = 0 or x = 7.

    106. | | ≥ 1
    It can be rewritten as

    For

    For

    So the solution is

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    https://brainmass.com/math/basic-algebra/determine-in-terms-of-an-inequalities-105299

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    Solution Preview

    Please see the attached file.

    9.1 52.
    [8x - 3(3x + 2)] - 5 ≥ 3(x + 4) - 2x

    First distribute it into the parenthesis, then move x into the left side of the inequality. Remember to change the sign if a negative number is multiplied or divided.
    CORRECT

    72. Elaine's height is 67 in. Determine, in terms of an inequality, those weights W that will keep her body mass index below 25.
    The body mass index is defined as

    Her height is 67 inches, and BMI <25

    Her weight has to be less than 159.64 pounds.
    CORRECT

    76. A long-distance telephone call using ...

    Solution Summary

    The solution provides explanations and discussion for the problems.

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