Question

Can someone help with this please? (x+18)(x-17)(x+17)>0

Answer 1

We know the zeroes are -18, -17, 17. Let's test the intervals (-infinity, -18), (-18, -17), (-17, 17), (17, infinity)

Answer 2

Would the result be positive or negative if you had x=-19

Answer 3

Sorry, my computer crashed earlier. The result is negative.

Answer 4

ok so we can discard that interval, because a negative number is less than 0

Answer 5

what about -17.5?

Answer 6

Again it is negative.

Answer 7

no, it's positive

Answer 8

positive * negative * negative=positive

Answer 9

Okay, I'm not understanding then. Is it possible for you to step me through the problem, or a similar one so that I can understand the process?

Answer 10

Ok, you know that a negative*positive =negative,
positive*positive=positive,
negative*negative=positive

Answer 11

Yes :)

Answer 12

That's all I'm doing here :)

Answer 13

We have the zeros of the function because it is in factored form

Answer 14

Where did you get -17.5? And what were you multiplying it with to make it a positive?

Answer 15

Look above, we're considering the intervals where the numbers can change signs

Answer 16

We have the 3 zeroes, so we make all possible intervals using those zeros

Answer 17

and select a random number from that interval to determine if using that number will make the entire expression positive or negative

Answer 18

understand?

Answer 19

I'm getting there. So when you used -17.5, it was the random number?

Answer 20

We have the x-intercepts. Yes, -17.5 was a random number in the interval
(-18,-17)

Answer 21

Because -17 and -18 are x-intercepts right next to each other, all values between them will either be above or below the x-axis (positive or negative)

Answer 22

Okay that makes sense.

Answer 23

Alright, we have the 4 intervals.

Answer 24

We've determined that (-infinity, -18) yielded a negative result, not part of the solution

Answer 25

(-18,-17) yielded positive, so -18<x<-17 is part of the solution. We have 2 more intervals.

Answer 26

What about a number in the interval (-17, 17)

Answer 27

That is a negative.

Answer 28

right, not part of the solution

Answer 29

what about (17, infinity)

Answer 30

Positive.

Answer 31

ok, now we have our answer. you know what it is?

Answer 32

It is either a solution set or all real numbers, but I'm not sure how to tell which.

Answer 33

Remember, we already found the answer by testing these intervals

Answer 34

Any interval where the result was positive is part of the solution

Answer 35

Oh! So it is a solution set.

Answer 36

yes

Answer 37

because every value in that interval will yield either positive or negative, no matter which random number you pick

Answer 38

We don't include the actual numbers themselves when testing because we already know they are the x-intercepts, or zeros of the cubic function

Answer 39

So how would I post my answer? \[{x l-18,17} \] like that?

Answer 40

Urgh it didn't put my brackets in

Answer 41

Are you familiar with set-builder notation or interval notation? Either one is fine. I prefer interval notation.

Answer 42

That's what i used above

Answer 43

No I'm not, I use equation editor in MS word but that is all I know.

Answer 44

\[(5, \infty)\]You've probably seen it plenty of times, set-builder looks like this:
{x|x>5}
Interval
\[(5, \infty)\]

Answer 45

Oh yes I see. How do you get the character for the absolute line?

Answer 46

Shift backslash

Answer 47

the one above the enter key

Answer 48

Oh I see it now.

Answer 49

So, because my solution is a set, would I write it as {x|x<-18,17}

Answer 50

In set builder:
{x|-18<x<-17 or x>17}
Interval:
\[(-18, -17)\text{U}(17, \infty)\]

Answer 51

The U stands for union between the intervals

Answer 52

Recall that we had 2 intervals that satisfied the inequality

Answer 53

x<-18 was not one of them

Answer 54

yes

Answer 55

x > -18 and x < -17 can be simplified to -18<x<-17

Answer 56

So do you understand now?

Answer 57

Well, I understand how we solved the problem yes. It still confuses me how I am supposed to answer. But I will try to the way you wrote it out in set builder.

Answer 58

how do you usually express your solutions?

Answer 59

Thats just it, this is for a fimal exam and I did these problems nine weeks ago. It is all done in MyMathLab so the program offers the correct format for you already. It is showing this for a solution set {x|__}

Answer 60

so set-builder

Answer 61

So I simply plug in -18<x<-17 or x>17 ?

Answer 62

And I can use the conjunction "or" within the set builder?

Answer 63

or is a disjunction, yes i believe you can use it in set-builder

Answer 64

i assume someone will be reviewing your answers? they'll know what you mean

Answer 65

Well, the program itself grades the exam, but I will do my best. Thank you so much for your time. You were very helpful, and I am glad that you didn't just give me the answer, I like to try and figure these things out, although I am not very good at it.

Answer 66

glad to help

Answer 67

:)

Answer 68

if you have a similar problem you'd like to practice with, i'll review it with you

Answer 69

I don't at the moment, but thank you for the offer :)

Answer 70

One more question, the answer is still -18 even though in the original equation it is a positive 18?

Answer 71

I think I've confused myself again .

Answer 72

if (x+18)=0, what is the zero?

Answer 73

Oh zero has to be negative.

Answer 74

(-18+18)=0, x=-18

Answer 75

Yeah, I pictured it on a number line in my head and then it made sense. Thank you again!

Answer 76

YW