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student1988

  • 2 years ago

Solve the inequality in terms of intervals. Interval notation (x + 4)(x − 3)(x + 8) ≥ 0

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  1. satellite73
    • 2 years ago
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    zeros are at \(-8,-4,3\) so divide the real line up in to four intervals \[(-\infty, -8),(-8,-4),(-4,3),(3,\infty)\] it is clearly positive on the last intervals, so it will be negative, positive, negative, positive in that order

  2. satellite73
    • 2 years ago
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    since you want to know where it is positive, pick the second and fourth interval. because it is \(\geq\) and not \(>\) use closed brackets to write the interval

  3. student1988
    • 2 years ago
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    I'm a little confused. What are the interval that satisfy the equation?

  4. satellite73
    • 2 years ago
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    the second and fourth one you can check by plugging in a number in either of those intervals, and see that it is positive

  5. student1988
    • 2 years ago
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    (-8,-4)U(3,infinity) ?

  6. student1988
    • 2 years ago
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    How did you come to this answer?

  7. satellite73
    • 2 years ago
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    well you need square brackets, not round ones

  8. satellite73
    • 2 years ago
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    \(>0\) is a synonym for "positive" if \(x>3\) then all the factors are positive, so their product is positive as well since it changes sign at the zeros, you know it is "negative" then "positive" then "negative" then "positive"

  9. satellite73
    • 2 years ago
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    you could also check by noting that if \(x<-8\) all the factors are negative since the product of three negative numbers is also negative, you know on \((-\infty,-8)\) the whole thing is negative

  10. satellite73
    • 2 years ago
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    but don't forget to use square brackets, not round ones

  11. student1988
    • 2 years ago
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    ok, thank you very much for your help! I don't have a book at this moment that explained inequalities and factoring and I am reviewing. You've been a great help. Thanks! :)

  12. satellite73
    • 2 years ago
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    yw

  13. davisla
    • 2 years ago
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    These are 2 older videos I made with similar examples. Perhaps they would help. www.mathmods.com/mat115/chapters/chapt2/Quadratic_Inequalities1/Quadratic_Inequalities1.html www.mathmods.com/mat115/chapters/chapt2/Quadratic_Inequalities_2/Quadratic_Inequalities_2.html

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