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student1988
 2 years ago
Solve the inequality in terms of intervals. Interval notation
(x + 4)(x − 3)(x + 8) ≥ 0
student1988
 2 years ago
Solve the inequality in terms of intervals. Interval notation (x + 4)(x − 3)(x + 8) ≥ 0

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satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2zeros 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2since 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

student1988
 2 years ago
Best ResponseYou've already chosen the best response.0I'm a little confused. What are the interval that satisfy the equation?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2the second and fourth one you can check by plugging in a number in either of those intervals, and see that it is positive

student1988
 2 years ago
Best ResponseYou've already chosen the best response.0(8,4)U(3,infinity) ?

student1988
 2 years ago
Best ResponseYou've already chosen the best response.0How did you come to this answer?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2well you need square brackets, not round ones

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2\(>0\) 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"

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2you 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.2but don't forget to use square brackets, not round ones

student1988
 2 years ago
Best ResponseYou've already chosen the best response.0ok, 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! :)

davisla
 2 years ago
Best ResponseYou've already chosen the best response.0These 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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