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Thread: 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 $\displaystyle x\geq 2/7 \,\,and \,\,x\leq 3$, then wouldn't $\displaystyle 2/7\leq x \leq 3$, so the interval would be $\displaystyle (2/7, 3)$
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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:
    (-∞,∞)
    $\displaystyle 3x \geq -4x + 2$

    $\displaystyle 7x \geq 2 $

    $\displaystyle x \geq \frac{2}{7}$

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


    $\displaystyle 5 \geq 3x - 4$

    $\displaystyle 9 \geq 3x $

    $\displaystyle 3 \geq x $

    $\displaystyle x \leq 3 $.


    Putting the inequalities together, we get

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


    In interval notation this is

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

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