Question

Solve the inequality in terms of intervals. Interval notation

(x + 4)(x − 3)(x + 8) ≥ 0

Answer 1

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

Answer 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

Answer 3

I'm a little confused. What are the interval that satisfy the equation?

Answer 4

the second and fourth one
you can check by plugging in a number in either of those intervals, and see that it is positive

Answer 5

(-8,-4)U(3,infinity) ?

Answer 6

How did you come to this answer?

Answer 7

well you need square brackets, not round ones

Answer 8

\(>0\) 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"

Answer 9

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

Answer 10

but don't forget to use square brackets, not round ones

Answer 11

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! :)

Answer 12

yw

Answer 13

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