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

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satellite73Best ResponseYou've already chosen the best response.2
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
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
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
 one year ago

student1988Best ResponseYou've already chosen the best response.0
I'm a little confused. What are the interval that satisfy the equation?
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
the second and fourth one you can check by plugging in a number in either of those intervals, and see that it is positive
 one year ago

student1988Best ResponseYou've already chosen the best response.0
(8,4)U(3,infinity) ?
 one year ago

student1988Best ResponseYou've already chosen the best response.0
How did you come to this answer?
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
well you need square brackets, not round ones
 one year ago

satellite73Best 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"
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
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
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
but don't forget to use square brackets, not round ones
 one year ago

student1988Best ResponseYou've already chosen the best response.0
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! :)
 one year ago

davislaBest ResponseYou've already chosen the best response.0
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
 one year ago
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