Question

How would you graph the inequality
y < -2 or y > 3?

Answer 1

I don't know how to incorporate the word 'or' into it..

Answer 2

Solutions can satisfy one or the other inequality.

Answer 3

So I just work for one and it will solve the other as well?

Answer 4

Think about it again in terms of collections of points..

You want all the points (h,k) where k < -2 or k > 3.

Answer 5

No you have to deal with both separately.

Answer 6

That's the problem I guess..each inequality is as simplified as it will go it seems to me...and I can't figure out how to graph both along with 'or'...

Answer 7

Pick a point, any point on the Cartesian plane.

Answer 8

3, on the x axis

Answer 9

Ok, so is the y part of (3,0) less than -2 or greater than 3?

Answer 10

neither?

Answer 11

It's a yes or no question.

Answer 12

oops...missed the y part in your explanation...hold on..

Answer 13

What is the y part of (3,0) ?

Answer 14

0?

Answer 15

Correct. Is 0 less than -2 or greater than 3?

Answer 16

neither..? zero is not greater than 3, nor less than negative two..

Answer 17

It is a yes or no question.

Answer 18

Is 0 less than -2 or greater than 3?

Answer 19

I don't think it's a yes or not question.

Answer 20

Ah. Then this is the problem

Answer 21

I picked the wrong number I'm guessing...:P

Answer 22

It is a yes or no question. A standard form of boolean logic.

Are you familiar with truth tables?

Answer 23

No, it's a fine number.

Answer 24

I'm not familiar with boolean logic or truth tables...I'm a rural hoosier girl from Indiana..

Answer 25

Is it true that you like being shot in the foot, or poked in the eye?

Answer 26

You're losing me..

Answer 27

Sorry, I'm giving another example.

Answer 28

Not intending to be mean. Just had to pick two things I was pretty certain you didn't like ;p

Answer 29

It's just not clicking...

Answer 30

Ok, lets try this.

Answer 31

Think of a number between 1 and 100.

Answer 32

25

Answer 33

Wait, do it again and don't tell me.

Answer 34

oh, got it...ok I've thought of a different number.

Answer 35

I will guess your number in less than 7 guesses.

Answer 36

If you can answer each of my questions with only a yes or a no.

Answer 37

Ready?

Answer 38

ok, whatever...I've got to get back to my math problem here soon though..

Answer 39

Is your number less than 25 or greater than 75?

Answer 40

neither.

Answer 41

You mean no.

Answer 42

No your number is not less than 25 or greater than 75

Answer 43

ok then, no.

Answer 44

Ok, so is your number less than 38 or greater than 63?

Answer 45

no

Answer 46

Is your number less than 45 or greater than 56?

Answer 47

no

Answer 48

Ok, is your number less than 48 or greater than 51?

Answer 49

no

Answer 50

Is your number 49 or 50?

Answer 51

50...so apart from being cool,..how does this apply to my math problem

Answer 52

You are supposed to answer yes or no. ;p

Answer 53

Is your number 49 or 50?

Answer 54

oops...yes then...

Answer 55

Good!

Answer 56

Ok, now that we've had some warming up..

Is 0 less than -2 or greater than 3?

Answer 57

Yes or no.

Answer 58

no

Answer 59

Is 7 less than -2 or greater than 3?

Answer 60

yes

Answer 61

Is -300 less than -2 or greater than 3?

Answer 62

yes

Answer 63

So lets look at the equality for a second.

What are the lines y = -2 or y = 3?

Answer 64

What do they look like?

Answer 65

two horizontal lines on the y axis?

Answer 66

through the y axis at the points (0,3) and (0,-2)

Answer 67

yeah I was thinking that too...was not sure how specific you wanted me to be..

Answer 68

Right? So now think about all the points above the top line y=3.

For those points is the y part greater than 3 or less than -2?

Answer 69

yes or no

Answer 70

yes

Answer 71

And for all the points below the line y = -2

Are the y values of those points greater than 3 or less than -2? (yes or no)

Answer 72

yes

Answer 73

And for the points in between those two lines..

Are the y values of those points greater than 3 or less than -2?

Answer 74

no

Answer 75

Great!

So the solution to the inequality

y < -2 or y > 3

Would be all the ones you said yes for. They are the points for which the y part is greater than 3 or less than -2.

Answer 76

Shade those regions (and use dotted/dashed lines for their edges because it's not greater than or equal to).

Answer 77

I did, thanks polpak.

Answer 78

So just remember that if you have multiple conditions joined by an 'or', the whole thing is true if any one of them is true. And false only if all are false.

Answer 79

ok then...to more math problems...I may be back on here tonight..dunno..

Answer 80

Ok, good luck. Thank you for your patience.