Question

what is the approximate value of the function at x = -4?

there is a graph.

Answer 1

this is the graph

Answer 2

So when we look over at x=-4, we try to figure out at what height the red line is located.
Looks like it's between 1 and 2 yes?
Maybe 1.75ish?

Answer 3

is it closer to 1.5 or 1.8? i'm assuming 1.8

Answer 4

Yah 1.8 sounds a little bit more accurate :)

Answer 5

It's probably 1.5 at around x=-6

Answer 6

i have another one so stay here!

Answer 7

what is the approximate value of the function at x = 2?

Answer 8

Hmm, so our red line is below the x-axis at x=2, right?
Take a guess! :)

Answer 9

either 0.25 or 0.50... positive or negative

Answer 10

Since it's below the x-axis, it will definitely be negative.
It's between -1 and 0.

Yah -0.25 seems like a good guess!

Answer 11

do you know how to do ones like :
solve x/(x-2) < 2

Answer 12

\[\Large \frac{x}{x-2}\lt2\]Let's ummmm, multiply both sides by x-2,\[\Large x \lt 2(x-2)\]Understand that step? :o
The (x-2)'s cancel on the left side.

Answer 13

yes.

Answer 14

so that leaves you with x < 2x - 4

Answer 15

then you put x on one side and get -x < - 4, then it becomes x > 4. correct answer?

Answer 16

Hmm one sec, yes that's part of our inequality.
I think we should be getting another part also though.

Lemme see what I messed up.

Answer 17

x > 4 could be a correct answer... i don't know why it wouldn't be. but let me know what you get.

Answer 18

Oh you have some multiple choice answers or no? :

Answer 19

no i don't.

Answer 20

oh :)

Answer 21

The problem is this...
Remember what happens when we multiply/divide across an inequality?
The inequality sign `flips` directions.

Example:\[\Large -3x \lt 6\]Dividing both sides by -3 gives us,\[\Large x>-2\]See how the sign changed from `less than` to `greater than` ?

Answer 22

yes, which i did that.

Answer 23

So in our problem, I think it's a bad idea to multiply both sides by (x-2) as I did.
We don't know whether or not that quantity is negative.
So let's try something else :O

Answer 24

okay

Answer 25

\[\Large \frac{x}{x-2}\lt2\]Subtracting 2 from each side,\[\Large \frac{x}{x-2}-2<0\]Let's get a common denominator:\[\Large \frac{x}{x-2}-\frac{2(x-2)}{x-2}\lt0\]

Answer 26

So what does that simplify down to? :)\[\Large \frac{x-2(x-2)}{x-2}<0\]

Answer 27

Hmm I hope I'm doing this right, man I hate inequalities lol.
Lemme check one of the smarty pants guys :P

@SithsAndGiggles @satellite73

Answer 28

let me know. im still confused

Answer 29

I don't think putting the 2 on the other side is really necessary. I'd go with
\[x<2(x-2)\]
which gives
\[x<2x-4\\
-x<-4\]
Either way works, but I think this is simpler. ;)

Answer 30

so that leaves you with x > 4. because you divide by -x and flip the inequality.

Answer 31

Well if you wolfram this, it gives 2 intervals, x<2, x>4.

So I was just getting a little confused :d

Answer 32

how did you get the two intervals? because thats' the answer i need

Answer 33

Because from this point, where I combined the fractions:\[\Large \frac{x-2(x-2)}{x-2}<0\]After we simplify, we get,\[\Large \frac{-x+4}{x-2}\lt0\]

Answer 34

If we look at the top and bottom separately (which I guess is what we're supposed to do),\[\Large -x+4\lt0 \qquad\qquad\qquad x-2\lt0\]

Answer 35

\[\Large -x+4\lt0 \qquad\to\qquad x>4\]\[\Large x-2\lt0 \quad\qquad\to\qquad x<2\]

Answer 36

That too confusing? :d
Or was it back when we combined the fractions the part you got stuck on?

Answer 37

this all just hurts my head. lord jesus help me

Answer 38

XD

Answer 39

alright one more question

Answer 40

k c:

Answer 41

that's an = sign and then a - sign

Answer 42

Solve for x?

Answer 43

yes

Answer 44

Note:\[\Large x^2+x \qquad=\qquad x(x+1)\]

Answer 45

\[\Large \frac{x+5}{x(x+1)}=\frac{1}{x(x+1)}-\frac{x-6}{x+1}\]

Answer 46

then what the heck do you do

Answer 47

If we multiply both sides by (x+1), can you see what will happen? :o

Answer 48

please write it out for me

Answer 49

Lemme give you a simpler example really quick :)
Maybe it will help it to click.\[\Large \frac{x}{3}=\frac{7}{3}\]
If we multiply both sides by 3, what does it give us?

Answer 50

x = 7

Answer 51

good, all of the denominator 3's cancel with the 3's that we multiplied through by, right?

Answer 52

yes

Answer 53

\[\frac{ x + 5 }{ x } = \frac{ 1 }{ x } - x - 6\]

Answer 54

then what

Answer 55

One small thing to be careful of.
We don't usually write it, but there is a pair of parenthesis implied when we have a negative in front of a fraction.\[\Large \frac{x+5}{x(x+1)}=\frac{1}{x(x+1)}-\frac{(x-6)}{x+1}\]

Answer 56

\[\Large \frac{ x + 5 }{ x } = \frac{ 1 }{ x } -(x - 6)\]

Answer 57

I got that. what next.

Answer 58

To finish getting rid of the fractions, let's multiply both sides by x.

Answer 59

Gives us something like this, yes? :)\[\Large (x+5)=1-x(x-6)\]

Answer 60

yes

Answer 61

From here, distribute your -x to each term in the brackets.
And then try to get everything to one side, so the other side =0

Answer 62

crap i gotta go :U sorryyyy :C gotta go take care of something