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

1. satellite73

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

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

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

4. satellite73

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

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

6. student1988

How did you come to this answer?

7. satellite73

well you need square brackets, not round ones

8. satellite73

$$>0$$ 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

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

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

11. student1988

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

yw

13. davisla