Question

Solve the following
\[\frac{3}{x+4} le 2\]
express as interval and graph

Answer 1

\[\frac{3}{x+4} \le 2\]

Answer 2

First - the exception would be \(x \ne -4\) as getting -4 in the place of x would get you undefined in the fraction.

Answer 3

Anyway, if you just kick out the exception — you can solve the inequality by multiplying x + 4 to both sides.

Answer 4

\( \color{Black}{\Rightarrow 3 \le 2(x + 4)}\)

\( \color{Black}{\Rightarrow 3 \le 2x + 8}\)

\( \color{Black}{\Rightarrow 3 - 8 \le 2x}\)

\( \color{Black}{\Rightarrow -5 \le 2x }\)

\( \color{Black}{\Rightarrow -2.5 \le x}\)

Answer 5

I thought you solve rational inequalities different...

Answer 6

No, not really.

Answer 7

\[3 \le 2x+8\]

Solve for x..

Answer 8

what if 2 was 0

Answer 9

I don't know what your question is.

Answer 10

Then no solution will be the answer..

Answer 11

As I told you - the exception to x is -4.

Answer 12

and 3 is not le or = 0...

Answer 13

\( \color{Black}{\Rightarrow (-\infty , -5]\cup [-3,+\infty) }\)

This is the interval notation.

Answer 14

\[\frac{3}{x+4}-2 \le 0\]
Figure out when the expression on the left is 0 and when it is undefeined
\[\frac{3-2(x+4)}{x+4} \le 0\]
\[\frac{3-2x-8}{x+4} \le 0\]
\[\frac{-2x-5}{x+4} \le 0\]

Answer 15

Then after you figure out when that expression of the left is undefined and zero you will test the intervals around each number to see when you have less than 0

Answer 16

so were only concerned about the denominator @myininaya

Answer 17

no that is not what i said

Answer 18

when the top is 0 and when the expression is undefined

Answer 19

when -2x-5=0
x+4=0

Answer 20

No! The bottom - not the top!

Answer 21

test around those numbers

Answer 22

:\ :{ :[

Answer 23

you already know -2x-5=0 will give you one value of x that satisfies the inequality because your expression also includes the equals part

Answer 24

Is the interval
[-4,-5/2]

Answer 25

x cannot be -4...

Answer 26

I told you the interval notation @purplec16

Answer 27

I don't see how you got that @ParthKohli

Answer 28

(-4,5/2]

Answer 29

-2x-5=0 when x=5/-2=-5/2
x+4=0 when x=-4

We already know -5/2 is part of the solution while -4 is not but we use these numbers to test around

-----|----|----
-4 -5/2

Answer 30

test outside the interval?

Answer 31

Plug in some number before -4
Plug in some number btw -4 and -5/2
Plug in some number after -5/2

And if the number you get is less than 0 then that interval is part of the solution

Answer 32

test the whole domain...

Answer 33

I did that... so is my answer correct?

Answer 34

\[\frac{-2x-5}{x+4} \le 0\]
A number before -4: I will do -100 for fun! :)
So \[\frac{-2(-100)-5}{-100+4}=\frac{200-5}{-96}=\frac{195}{-96} <0\]
This interval works
Now you try the second interval and third interval
(we only have three intervals to look at )

Answer 35

I still don't see the answer? (-infity, -4)U(-4,5/2]U[5/2,infity)

Answer 36

No one ever gave you the answer
We are trying to help you get the answer on your own
Do you not understand what I'm asking you?

Answer 37

nope...

Answer 38

to do*

Answer 39

Ok I tried the first interval
do you see that?

Answer 40

I did what you ask and that's what I got, it's not correct?

Answer 41

why do you have 5/2 in there?

Answer 42

-5/2 was the zero

Answer 43

This is what I said to do

Plug in some number before -4
Plug in some number btw -4 and -5/2
Plug in some number after -5/2

And if the number you get is less than 0 then that interval is part of the solution

Answer 44

(-infity, -4)U(-4,-5/2]U[-5/2,infity)

Answer 45

Then I did the first interval which were the numbers before -4 for you

Answer 46

darn it! I got the aw snap page :(
Okay yeah that works!

Answer 47

So am right :D

Answer 48

So am right :D?

Answer 49

no i'm sorry
try -3 what did you get
i was talking about the page sorry

Answer 50

One of your intervals is wrong is what I'm saying

Answer 51

if you plug in a value btw -4 and -5/2 what do you get ?

Answer 52

1

Answer 53

0

Answer 54

no 1 is right
not 0
that is bigger than zero so that does not work with our inequality

Answer 55

so what can we say about that interval?

Answer 56

well undefined...

Answer 57

0 for -5/2 and undefined for -4

Answer 58

no 1 you plug in -3 you get 1
not 0 and not undefined

Answer 59

no....

Answer 60

i said plug in a number btw those numbers

Answer 61

I really don't know what to say about this interval...

Answer 62

\[(-\infty,-4)U(-\frac{5}{2},\infty)\]

Answer 63

ok please try to do what i say: Plug in a number between -4 and -5/2 into the expression
\[\frac{-2x-5}{x+4}\]
We are looking at the middle interval right now
We are looking at (-4,-5/2] to see if it should be included in the answer
I picked a number for you that number being -3
Now if you plug in that number -3 into \frac{-2x-5}{x+4}\]
You will get what you said which was 1
and 1 is bigger than 0 not less than 0
So we do not include the second interval
make sure you include your zeros of \frac{-2x-5}{x+4}\]
Remember x=-5/2 was a zero so it should be included
Your answer is lacking a little