anonymous
  • anonymous
Solve the inequality in terms of intervals. Interval notation (x + 4)(x − 3)(x + 8) ≥ 0
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
I'm a little confused. What are the interval that satisfy the equation?

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anonymous
  • anonymous
the second and fourth one you can check by plugging in a number in either of those intervals, and see that it is positive
anonymous
  • anonymous
(-8,-4)U(3,infinity) ?
anonymous
  • anonymous
How did you come to this answer?
anonymous
  • anonymous
well you need square brackets, not round ones
anonymous
  • anonymous
\(>0\) 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"
anonymous
  • anonymous
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
anonymous
  • anonymous
but don't forget to use square brackets, not round ones
anonymous
  • anonymous
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! :)
anonymous
  • anonymous
yw
anonymous
  • anonymous
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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