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Math Help - Interval Notation Check

  1. #1
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    Interval Notation Check

    Solve the compound inequality:
    3x >= -4x+2 and 5 >= 3x-4


    Could someone check my work I am not sure if my interval notation is right.
    My solution:
    x>=2/7 & x<3

    Give the result in interval notation:
    (-∞,∞)
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  2. #2
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    If x\geq 2/7 \,\,and \,\,x\leq 3, then wouldn't 2/7\leq x \leq 3, so the interval would be (2/7, 3)
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  3. #3
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    Quote Originally Posted by Maxwell View Post
    Solve the compound inequality:
    3x >= -4x+2 and 5 >= 3x-4

    Could someone check my work I am not sure if my interval notation is right.
    My solution:
    x>=2/7 & x<3

    Give the result in interval notation:
    (-∞,∞)
    3x \geq -4x + 2

    7x \geq 2

    x \geq \frac{2}{7}

    \frac{2}{7} \leq x.


    5 \geq 3x - 4

    9 \geq 3x

    3 \geq x

    x \leq 3 .


    Putting the inequalities together, we get

    \frac{2}{7} \leq x \leq 3.


    In interval notation this is

    x \in [\frac{2}{7},3] .

    You have to use the square brackets because you CAN include the endpoints.
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