## student1988 Group Title Solve the inequality in terms of intervals. Interval notation (x + 4)(x − 3)(x + 8) ≥ 0 one year ago one year ago

1. satellite73 Group Title

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 Group Title

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 Group Title

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

4. satellite73 Group Title

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 Group Title

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

6. student1988 Group Title

How did you come to this answer?

7. satellite73 Group Title

well you need square brackets, not round ones

8. satellite73 Group Title

$$>0$$ 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 Group Title

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 Group Title

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

11. student1988 Group Title

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 Group Title

yw

13. davisla Group Title