Question

2x+11>25

Answer 1

subtract 11 from both sides first..what do you get?

Answer 2

2x>14

Answer 3

right. now divide both sides by 2

Answer 4

x>7 is this written in interval notation?

Answer 5

nope

Answer 6

interval notation would be \((7,\infty)\)

Answer 7

how do i figure that?

Answer 8

x > 7 right?

Answer 9

yes but the interval notation how do i figure that part

Answer 10

that means x is GREATER than 7.., so your numbers are 7 above...that's why you have 7, infinity

then it's > sign so you just use parentheses...that's why (7,infinity)

got it?

Answer 11

okay so it is just another way to say x>7 ?

Answer 12

yep

Answer 13

awesome! thankyou!!!

Answer 14

welcome

Answer 15

Interval notation describes an interval on the real number line

So when we say

(A, B)

we mean the interval from A to B where we are NOT including neither A nor B

Ex:

(7,20)

describes the interval from 7 to 20 (excluding both endpoints)

Answer 16

so you shade in between the two points and not the points themselves?

Answer 17

exactly

Answer 18

the endpoints are open circles to visually show they are NOT included in the interval

Answer 19

In your case,

(7,infinity)

means that you have an interval where you start at 7, but there is no right endpoint since infinity goes on forever

you're NOT including 7, so you draw an open circle here

Answer 20

how do i translate this into other problems as well? like i tried another and it didnt work. -3x isgreater than or equal to 15

Answer 21

-3x >= 15

Divide both sides by -3

x <= -5

Notice how the sign flips

Answer 22

The answer in interval notation is

(-infinity, -5]

and you graph this by plotting a closed circle at -5, then you shade to the left

Answer 23

but how do i know what side of the ( ,) to put infinity

Answer 24

when you say x <= -5, you mean "anything less than or equal to -5"

So you're describing the interval

-infinity to -5 , ***include the -5***

which translates to

(-infinity, -5]

in interval notation

Answer 25

so if i am using a < sign then the number goes on the right and if i am using a > sign the number goes on the left side of the ( )

Answer 26

yes,

if you have x > something, then it translates to

(something, infinity)

-------------------------------------------------------

if you have x < something, then it translates to

(-infinity, something)

Answer 27

so if infinity comes first it is negative? always?

Answer 28

yes, you read from left to right, so something like

(infinity, 2)

doesn't make sense (since it's backwards)

Answer 29

how do i know if i even use infinity i just tried another with infinity and the computer told me no and showed me the right answer with out infinity

Answer 30

if you have something like

2 < x < 10

then the interval doesn't stretch forever in one direction and you will NOT use infinity in the interval notation

Answer 31

is it okay to have negative numbers or is it better to switch the sign and get rid of the negative

Answer 32

what do you mean

Answer 33

x<-7/5 . can i just flip the sign and make it x>7/5

Answer 34

no, you can't do that

Answer 35

you can only flip the sign when going from

-5x < 7

to

x > -7/5

Answer 36

basically when you multiply/divide both sides by a negative number

Answer 37

why did it get switched in the earlier problem then

Answer 38

because I divide both sides by -3

Answer 39

-3x >= 15

x <= -5

Answer 40

oh okay. is set builder and interval notationthe same?

Answer 41

no, they describe the same thing though

Answer 42

then how do i write it for x<= -1/6

Answer 43

interval notation:

(-infinity, -1/6]

set-builder notation

{x | x<= -1/6}


set-builder notation is basically writing the same thing again, but in a much more mathematically fancy way

Answer 44

so the interval notation is writen in a way that is easier to graph by looking at it?

Answer 45

thats one way you can think of it

Answer 46

but some may find set-builder easier

Answer 47

depends on how you look at it really

Answer 48

am i just making a simple error or something in this one cause the computer program keeps telling me it is wrong. 11x-14<=5x-15 i got x<=-1/6 but it is saying that is wrong.. i put it in set builder notation {xl<=-1/6}

Answer 49

you forgot an x

Answer 50

{xl<=-1/6}

should be

{xlx<=-1/6}

Answer 51

and then when i put it in interval notation it would be (-1/6,infinity)?

Answer 52

(-infinity, -1/6]

Answer 53

i thought infinity went second when x <= a number

Answer 54

no

if you have x >= something, then it translates to

[something, infinity)

-------------------------------------------------------

if you have x <= something, then it translates to

(-infinity, something]

Answer 55

does the [ always go with the side the number is on?

Answer 56

yes, it can't go with negative infinity or positive infinity because you cannot include infinity in the interval

Answer 57

how do i know when to use a set of ( ) rather than [ )

Answer 58

Use ( to exclude

Use [ to include

Answer 59

but if i have x>8 how does that tell em if i need ot include or exclude?

Answer 60

so for example

(8, infinity) means exclude 8 and include everything larger than 8

[8, infinity) means include 8 and include everything larger than 8

Answer 61

therefore, x > 8 means (8, infinity)

Answer 62

but how because i dont see a difference in x>8 from any other problem like as far as knowing if it is ( ) or with a braket

Answer 63

> means strictly greater than

Answer 64

so we are NOT including 8

Answer 65

oh my goodness i was making that a lot harder than it is

Answer 66

that's ok, it's making sense now right?

Answer 67

yes! thankyou so much!

Answer 68

you're welcome