Question

could someone please help me with number 4b) in the attached file ? please and thank you :)

Answer 1

cross multiply

Answer 2

when i checked the answer guide i was given by my teacher... it said (x+5) instead of (2x+10) to cross multiply

Answer 3

\[\large \frac 1{2x + 10} \implies \frac 1{2(x+5)}\]
do you see why now?

Answer 4

it doesn't really make any difference

Answer 5

oohh.. so this is the answer it gives me in the guide.

Answer 6

i think i'd like to object to that solution... i don't think 1/2(x+5) is equal to 1/x+ 5 riight @Hero ?

Answer 7

inconsistently though, 2x + 10 gets brought back to the solution. this may be right...but i doubt it's a good solution...it uses too many segues

Answer 8

segues?

Answer 9

yeah i got confused when i looked at it

Answer 10

segues means it deviates from the direct solution a lot

Answer 11

@xlegendx oh okay. so should i just stick to 2x+10

Answer 12

i would have done this:

\[\frac 1{2x + 10} < \frac 1{x+3}\]
\[x + 3 < 2x + 10\]
\[0 < 2x + 10 - x - 3\]
\[0 < x + 7\]
\[x > -7\]

Answer 13

then of course your limits are 2x + 10 = 0 and x + 3 = 0

Answer 14

it gives the same answer with your solution guide

Answer 15

so i suppose my earlier comment about its being wrong is wrong

Answer 16

For some reason I started using equal signs toward the end

Answer 17

i was thinking you intended that to see if the asker was really paying attention to the solution

Answer 18

sorry... im getting a little lost. :S

Answer 19

we were just doing alternate solutions to the problem. showing you that there are more simple solutions than the one in your guide

Answer 20

frankly, i think it made a typographical error...because mathematically, there is no way for 2 to disappear and reappear

Answer 21

oh okay. and yeah alright. i thought something about it looked funny :S

Answer 22

\[\frac{ 1 }{ 2x+10 }<\frac{ 1 }{ x+3 }\]
then substract by
\[\frac{ 1 }{ x+3 }\]
you'll get
\[\frac{ 1 }{ 2x+10 }-\frac{ 1 }{ x+3 }<0\]
now add 'em
\[\frac{ 1*(x+3) }{ (2x+10)(x+3) }-\frac{ (2x+10)*1 }{ (2x+10)(x+3) }<0\]
\[\frac{ x+3-2x-10 }{ (2x+10)(x+3) }<0\]
sums up every term
\[\frac{ -x-7 }{ (2x+10)(x+3) }<0\]
Multiply both sides by -2 and factorize 2x+10 by 2
\[\frac{ -2*(-x-7) }{ 2(x+5)(x+3) }<0\]
do magic
\[\frac{ x+7 }{ (x+5)(x+3) }<0\]
Now to solve this you can use a method with a sign chart

(I don't know if you know how to use that chart, but i'll asume you do, if you don't, please tell me
So, your answer will be
x<-7 U -5<x<-3

Answer 23

wow that was hard worked

Answer 24

Other than the one @Umangiasd posted

Answer 25

woaaah!! okay! wow thanks @xlegendx @Hero @Umangiasd

Answer 26

interesting though is that even @Umangiasd 's solution doesn't show the disappearing 2

Answer 27

You can't just go around cross multiplying when you have inequalities, care there!!

Answer 28

-6 is greater than -7 though...

Answer 29

The correct solution is here

Answer 30

http://www.wolframalpha.com/input/?i=1%2F%282x+%2B+10%29+%3C+1%2F%28x+%2B+3%29

Answer 31

i meant x>-7, which is the solution you found before asdsad xD

Answer 32

that makes it correct then... -1/2 is greater than -1/3

Answer 33

or maybe im wrong

Answer 34

maybe we are all wrong here XD

Answer 35

You're supposed to use @xlegendx method to find one of the x's. Then use critical points to find the rest.

Answer 36

When you multiplied by 2.. wouldnt it be x+14 ... not x+7 ? :S

Answer 37

is it about time we called satellite @Umangiasd ? lol

Answer 38

oh yes, i actually made a mistake when i multiplied by -2 you have to change the sign too
you have \[\frac{ x+7 }{ (x+5)(x+3) }>0\] and using the chart you obtain the actual solution xD (use the positives)

Answer 39

i think this is beginning to get overcomplicated :))

Answer 40

@xlegendx as much as i appreciate all the help from everyone... i agree with what you just said xD

Answer 41

what's common with what we all said though is that x > -7 and -5 < x < -3

Answer 42

actually...im not sure with -5 < x < -3 since x > -7 doesn't fit there. man, i'm getting confused too

Answer 43

here's the full answer the guide gave me :S

Answer 44

alll i know is x > 7 and x \(\ne\) -5 and x\(\ne\) -3

Answer 45

ah there it is

Answer 46

@Umangiasd just made a mistake in the range.

Answer 47

yup xD when mutiplying by -2 in the large comment i made i keep the sign as < and should have turned it into > ^^!

Answer 48

so problem solved (at least for us...i think @alexeis_nicole is still confused)

Answer 49

i kinda am :S sorry!!

Answer 50

do you get @Umangiasd solution? since it's the one closest to the guide

Answer 51

soo.... if you multiply by -2 this is what it looks like right?

\[-2\left( \frac{ -x-7 }{ 2(x+5)(x+3) } \right)\]

Answer 52

nevermind im confused

Answer 53

That solution is messed up. It' not right

Answer 54

Yes and that is >0
then cancel the "2" and enter the minus
you'll get
\[\frac{ x+7 }{ (x+5)(x+3)}>0\]
then use the chart, find the "pluses" and you'll obtain the same as wolfram

Answer 55

The second step should be

\[\frac{1}{x + 5} - \frac{2}{x + 3} < 0\]

Answer 56

I'm referring to the solution that @alexeis_nicole posted originally

Answer 57

@Umangiasd :)