Question

8Ix+3/4I <2
A. x<-1 5/6 or 5/6
B .x= -1 or x= 41/3
C. x= -1 5/6 or 4 1/3
D. x= -1 5/6 or X= -1

Answer 1

okay let's play this game hehe
the game says first divide both side of the inequality by 8

Answer 2

is 1.5 the same as 1/2

Answer 3

Now next step is matching this with another rule of the game
with is if |x|<a then -a<x<a this is called conjunction

Answer 4

Nope!

Answer 5

8Ix+3/4I <2
Ix+3/4I <1/4
So x+3/4<1/4
and x+3/4 >-1/4

So x<-0.5 and x>-1
x (-1, -0.5)

Answer 6

1.5 is 3/2
1/2=0.5 surely 3/2>1/2

Answer 7

@WilliamZhang pls do not give complete answers!

Answer 8

okay so where are we at in the equation

Answer 9

so can you apply the rules of this game to this?

Answer 10

no...

Answer 11

we said first divide by 8 both sides
then look at what case do we have

Answer 12

4

Answer 13

if |x|<a conjunction then -a<x<a

Answer 14

a must be positive though to apply this!
just a warning

Answer 15

so then it would be C

Answer 16

man! do the word and see what you get

Answer 17

work*

Answer 18

Do you want to play the game or not?
if not! no answer for you

Answer 19

think of this as a game will ya!

Answer 20

well im trying to figure out but I don't think the game is working

Answer 21

well the game is good to me!
we started at \(8|x+\frac{3}{4}|<2\)
dividig by 8
\( \large\frac{8}{8}|x+\frac{3}{4}|<\frac{2}{8}\)
8/8 is just 1
so
\( |x+\frac{3}{4}|<\frac{1}{4}\)
2/8 is 1/4 the game said so haha
no you have conjuction

Answer 22

Simplify the inequality ,
Then,if |A|<B
then -B<A<B.
Do the simple algebra. Thats it.

Answer 23

now* not "n" sorry

Answer 24

well! how about you continue this game?

Answer 25

k

Answer 26

so according to our game rule what should we do next?

Answer 27

add

Answer 28

add what
i will repost the games rule
if |x|<a, a is positive
then -a<x<a

Answer 29

I keep saying this many times you pay attention to it^_^

Answer 30

a is our case is 1/4
x is our case is x+3/4

Answer 31

can you see it now?

Answer 32

so divide the 3/4 to 1/4

Answer 33

in our case*
sorry for bad miss spelling

Answer 34

No!
look
|x|<a, so is becomes -a<x<a

Answer 35

instead of a put 1/4
instead of x put x+3/4

Answer 36

so x+ 3/4 <1/4

Answer 37

but i want you to remember that a should be positive to do this
rule otherwise we would have done a different thing! just keep this in mind for future problems^_^

Answer 38

what about the other side of the inequality?
-a<x<a
look and see if you did the right thing?

Answer 39

-1< x<-0.5 ,
A. x<-1 5/6 or 5/6
B .x= -1 or x= 41/3
C. x= -1 5/6 or 4 1/3
D. x= -1 5/6 or X= -1
so no above is correct.

Answer 40

@WilliamZhang pls no answers don't confuse our friend
we trying to learn this. we are not trying to just solve it?

Answer 41

we teach me how i fish not give me the fish lol
if you give me the fish next time you are not around i cannot get the fish

Answer 42

Sorry, I am just confused about the options.

Answer 43

we will see it through if there is anything but let's keep it simple for now

Answer 44

@WilliamZhang A <-1 or X >-1/2
B -5/32<x<5/32
C -1 ,x, -1/2
D is <-5/32 or x> 5/32

Answer 45

sorry I typed out something different

Answer 46

i figured out that! So i was gonna ask you to relook at
but that was not important for now!

Answer 47

once we get the right thing you would look at the answer and you will say look
that is the what i got too in this game lol

Answer 48

so its positive we know that

Answer 49

now pls go back to where we are
you said x+3/4<1/4
but i said that's not complete?

Answer 50

so it would be B

Answer 51

8|A|<2
|A|<2/8
|A|<(2*1)/(2*4)
|A|<1/4
U get it?
Then,
if |A|<B
then -B<A<B. U have to remember this.

Answer 52

Again you said be! i don't really care whether is A or B or C or D
our main focus is to solve this.

Answer 53

and learn how to do it!

Answer 54

1/4< x=3/4 <14

Answer 55

in fact i haven't looked at the solution yet haha.

Answer 56

so we would divde

Answer 57

that is incorrect! relook at it again?

Answer 58

that's how I just learned it

Answer 59

i said -a<x<a

Answer 60

-1/4 <3/4x <1/4

Answer 61

that is okay! learning take time! don't be afraid! ashamed or anything! okay
just continue learning. no matter say i have to learn it

Answer 62

you have x+3/4 how did it become 3/4x?

Answer 63

that's what I meant

Answer 64

the other parts are fine^_^

Answer 65

okay! be very precise! math is precise^_^
so -1/4<x+3/4<1/4

Answer 66

so divide -1/4and 3/4

Answer 67

now we want to separate x by it self
so we need to subtract 3/4
but we need to subtract it from all side

Answer 68

so subtract 3/4 by 1/4

Answer 69

Not divide!
we don't have multiplication to divide
we have addition here so subtraction is needed

Answer 70

look at this -1/4-3/4<x+3/4-3/4<1/4-3/4