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Math Help - compound inequality

  1. #1
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    inequality

    Solve the compound inequality and write answer in INTERVAL notation:
    5x > -9 + 2x and 9 2x >11



    (please help with one more)Solve





    The equation y = 0.50x + 8 represents the cost, y, in dollars of a medium pizza at a local restaurant, where x represents the number of toppings.
    (a) what is the y-intercept for this model and what does it represent in real-life?

    (b) what is the slope of this model and what does this represent in terms of the cost of a pizza?





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  2. #2
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    Lightbulb interval notation

    Quote Originally Posted by leleirvin
    Solve the compound inequality and write answer in INTERVAL notation:
    5x > -9 + 2x and 9 2x >11
    5x > -9 + 2x
    3x > -9
    .x > -3

    9 2x > 11
    ....
    -2x > 2
    .....-x > 1
    ......
    x < -1 (thanks rgep!)

    So we know that x must be greater than -3 and x must be less than -1. I beleive in interval notation that looks like this:

    (-3,-1)
    Last edited by Math Help; July 17th 2005 at 08:54 AM.
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  3. #3
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    Oops!

    -x > 1
    x < -1

    so the values of x satisfy -3 < x, x < -1 which is the interval (-3,-1)
    (round brackets because the endpoints are not included).
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  4. #4
    Site Founder Math Help's Avatar
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    Lightbulb

    Quote Originally Posted by leleirvin
    The equation y = 0.50x + 8 represents the cost, y, in dollars of a medium pizza at a local restaurant, where x represents the number of toppings.
    (a) what is the y-intercept for this model and what does it represent in real-life?

    (b) what is the slope of this model and what does this represent in terms of the cost of a pizza?
    A)
    y = 0.50x + 8

    first find the y-intercept (or when x=0)

    y = 0.50*(0) + 8

    y = 8

    Since x represents the number of toppings and y represents the cost of pizza, the y-intercept represents the cost of a pizza with no toppings. Since you can't have negative toppings this also represents the cheapest pizza you can have.


    B)
    y = 0.50x + 8 is in the form y = mx + b, where m is the slope.

    In this case the slope = 0.5 which is the cost per additional topping for a pizza.
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