Question

someone please help.
Which conjunction or disjunction is equivalent to the given absolute value inequality?

|x + 2| < 18

a. x + 2 > 18 or x + 2 < 18

b. x + 2 > 18 and x + 2 < 18

c. x + 2 < 18 or x + 2 > 18

d. x + 2 < 18 and x + 2 > 18

Answer 1

\(|x+2|<18\\\implies-18<x+2<18\\\implies-18-2<x<18-2\\\implies-20<x<16\)

So, \(|x+2|<18\implies x+2 < 18 \) and \( x+2 > -18\)

I don't see that option among yours.

Answer 2

the negitives didnt go tthru. u are correct :)

Answer 3

Ok.

Answer 4

thanks:)

Answer 5

You're welcome :)

Answer 6

You should close this one and give me a medal or something, otherwise people will just come and and look at this problem and see that it is solved. It's up to you ;)

Answer 7

lol how do u give medals?

Answer 8

When you click on "Best Response" that's a medal. You just gave me a one. :)

Answer 9

ohh hah sweet can u help my with another similar problem but walk me thru it pleaese?

Answer 10

But if you decide later that you don't like me, you can take it back and give it to someone else :( But you won't do that, right?

Answer 11

haha i will not :)

Answer 12

I'm here for you, at least for a little while

Answer 13

okay thanks so much :))))

Answer 14

k, shoot

Answer 15

okay l x l < 3

Answer 16

how would u do that if ur solving for the same thing as the first problem?

Answer 17

If I need to leave, feel free to send me a note

\(|x|<3\) means this: \(-3 < x < 3\). It's THAT easy!

Now, \(-3 < x < 3\) means: \(x < 3 \) and \(x > -3\).

ALWAYS the same pattern.

Answer 18

So if you had something else other than "x", just replace EVERYTHING between the "| |" where I have "x" above and repeat. Say you had |x +2| < 3, this means:

$$
|x+2| < 3
-3 < x+2 < 3
$$
Notice when I put the -3 there I REMOVED the "| |" part?

Answer 19

Let me rewrite that equation:

$$
|x+2| < 3\\
\text{ means}\\
-3 < x+2 < 3
$$

Answer 20

thankss so muchh :))

Answer 21

Does it make sense? Really?

Answer 22

yesss

Answer 23

k

Answer 24

okay im having trouble with another one but the multiple choice dosnt look formilar.. its in a different format :(

Answer 25

|2x + 3| < 11

Answer 26

and the choices areee...

Answer 27

ok well that didnt work.. imma try to type it

Answer 28

a. xE (-7,4)

Answer 29

k

Answer 30

b. (-14,8)

Answer 31

Link above says "access denied, you need super human capabilities to access" or something like that

Answer 32

c. (11,infinity)

Answer 33

lol iknow thats why im just typing it :0

Answer 34

or d. (-8,11)

Answer 35

|2x + 3| < 11

Ok, imma let you do this

What does it mean and REALLY try please!! And don't get mad at me an revoke my medal

Answer 36

x is less than 11.. ? right

Answer 37

2x + 3 < 11

That's the 1st step, what else?

Answer 38

do u have to do 3-3 and 11-3? .. or no

Answer 39

Not yet

Answer 40

o

Answer 41

2nd step:

-11 < 2x + 3

See that? Same pattern.

Answer 42

Where did the -11 come from?

Answer 43

because u subtracted it from 11

Answer 44

Whenever you have something like |blah blah blah| < something

This means - something < blah blah blah AND blah blah blah < something

Answer 45

ohh i get it now

Answer 46

So, "something" here is "11"

Answer 47

That's why the -11

Answer 48

so it became "-something"

Answer 49

yay!!!!

Answer 50

whats the next step

Answer 51

ok

So we have

$$
|2x + 3|<11\\
-11 < 2x+3 < 11
$$

Now we need to rearrange the blah blah part so that we only have "x" by itself there. We do that by 1st subtracting -3 from -11 and from 2x +3 and from 11 like this:

\(-11 -3< 2x+3 -3< 11-3\)

This gets rid of the 3 in the blah blah part of the equation

Answer 52

Now we have:

-14 <2x<8

Answer 53

See that?

Answer 54

yesss.

Answer 55

But we don't have x by itself yet. how do we make it so x is there alone in the center. We have 2x and we want to make it "x" alone. What do we need to do?

Answer 56

What can we divide 2x by to get just "x"?

Answer 57

2

Answer 58

do u do that to -4 and 8 too?

Answer 59

yep.

BUT, whatever we do to 2x we also must do to those endpoints, which we are calling "something"

I see you already saw that coming!! Nice. Nice!!!

Answer 60

Do it!!

Answer 61

:) haha but how do u solve for y?

Answer 62

then i have -2<x<4

Answer 63

Finish the problem! Your are practically there. No, don't solve for anything, just divide

Answer 64

--^

Answer 65

-14 <2x<8

Dividing EVERYTHING by 2, we get

-14/2 < 2x/2 < 8/2

Please, you can do this... what ya get?

Answer 66

oops i did -4/2 instead of -14

Answer 67

well?

Answer 68

-7<x<4

Answer 69

yaaaay!!!

Answer 70

So this means what?

Answer 71

something is less than something AND -something is less than something...

Help me...

Answer 72

-7, 4 !! :D

Answer 73

yesss omg thank u so much :D

Answer 74

Yea, -7 < x AND x < 4, Right?

Answer 75

you get a medal!!

Answer 76

right, thanks so much. ur an awesome teacherrrrr!:)

Answer 77

It's slow to learn but better to do it yourself and understand

Answer 78

ur awesome, too

Answer 79

yeah.. the school that im attending is k12 and i pretty much have to teach myself everything and it sucksks :(

Answer 80

It was a pleasure helping you

Answer 81

if i ever need help in the future can i messga u ?

Answer 82

:)

Answer 83

yep, anytime

Answer 84

sweet :D

Answer 85

sweet

Answer 86

take care

Answer 87

you tooo!