Question

Medal/Fan <3

Which conjunction or disjunction equivalent to the open sentence 4 –3|n + 2| ≥ 1?

A.
n + 2 ≥ 1 and n + 2 ≤ –1

B.
n + 2 ≤ 1 and n + 2 ≥ –1

C.
n + 2 ≤ 1 and n − 2 ≥ −1

D.
n + 2 ≥ 1 or n – 2 ≤ 1

Answer 1

First get the abs value alone, by subtracting 4 on both sides

Answer 2

@amoodarya @jdoe0001 @pgpilot326 @ehuman

Answer 3

4 –3|n + 2| ≥ 1
–3|n + 2| ≥ 1-4
–3|n + 2| ≥ -3 divide by -3
|n + 2| <= 1

Answer 4

|a|<b mean
-b<a<b
can you go on ?

Answer 5

okay @agent0smith ...

Answer 6

Alright.

Answer 7

sorry, forgot a negative\[\large \left| ax + b \right| \le c \] \[\large -c \le ax + b \le c \]

Answer 8

You have \[\large \left| n+2 \right|\le 1\]so use the above

Answer 9

Okay I get you. But I need an answer. Not just giving me the answer but I need to figure this out.

Answer 10

So try it using the last two posts. All you have to do is compare them.

Answer 11

\[\large \left| ax + b \right| \le c \]you have \[\large \left| n+2 \right|\le 1\] \[\large -c \le ax + b \le c\]so you'll have...

Answer 12

do you understand why the sign switches directions when you multiply or divide both side of an inequality by a negative number?

Answer 13

Nope... I'm finna get all F's that's why I'm studying.

Answer 14

so let's make it easy and start with something we know is true, like \(-1 < 1\). this is true, yeah?

Answer 15

Yes.

Answer 16

now what happens when we multiply both sides by -1? what's on the left and what's on the right?

Answer 17

umm this is where I get lost.

Answer 18

what's -1 x -1?

Answer 19

1

Answer 20

very good. and what's -1 x 1?

Answer 21

-1 ?

Answer 22

yep

Answer 23

now let's look at this all together...
\[-1<1\]\[(-1)(-1)\overset{?}{<}(-1)(1)\]\[\Rightarrow 1\overset{?}{<}-1\]\[\Rightarrow 1>-1\]
sign is switched whne we mulitply by a negative!

Answer 24

Ahhhh okay.

Answer 25

so from our original we have...
\[4-3|n+2|\ge 1\] and subtracting 4 from both sides we get \[-3|n+2|\ge -3\] and now we divide both sides by -3 and switch the sign because we're dividing by a negative \[|n+2|\le 1\]
and so we have isolated the absolute value!

do you follow this?

Answer 26

Okay I'm following but I'm still a few feet behind.

Answer 27

take a minute and get there. i don't want to lose you. and if you have a question about a step or steps, please ask!

Answer 28

Okay what exactly is "isolated" ???

Answer 29

Isolated means alone.

Answer 30

isolated means by itself.

Answer 31

Mkay cool so I got it

Answer 32

do you see in the last step how |n+2| is isolated? nothing else on its side?

Answer 33

Yes, sir.

Answer 34

I'm assuming you're a sir.

Answer 35

okay, so now remember the circle?

Answer 36

Yes.

Answer 37

i'm a man, but not a sir. i havne't been knighted and didn't serve in the military.

Answer 38

so draw the line, make the circle and remember what you're looking for.

Answer 39

Oh okay... I live in Cali but my parents are from the south so I automatically assume all men are "sirs".

Answer 40

so to be inside the circle, n+2 must be less than 1 AND greater than -1.


so to be on the circle, n+2 must be equal to 1 OR equal to -1.


so to be outside the circle, n+2 must be greater than 1 OR less than -1.

Answer 41

i live in "Cali" too and even though I'm in southern "Cali" it's not considered the south. silly civil war thing.

Answer 42

haha I meant southeast. :)

Answer 43

i know.

is the problem making sense? the approach and solution?

Answer 44

Yes it's making sense. :D And I'm in SoCal, too.

Answer 45

lol, the south is being frozen right now and we're in the 70's... how lucky are we?

Answer 46

VERY! My grandpa is sending me hate mail. He hopes everyone in SoCal gets worms or something.

Answer 47

yuck! what a nice guy! sic

Answer 48

Haha I still love him :) anyways, back on track.

Answer 49

you good on this one?

Answer 50

well I think so but is the answer D...? that runs in the family-understanding but getting the wrong answers. :/

Answer 51

look back at what we did and then select the answer that matches what we came up with

Answer 52

Oh duh.

Answer 53

So I'm assuming (I assume too much) the answer is A?