anonymous
  • anonymous
Can someone PLEASE help me out with Inequality? SOS
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
\[X>7 or -2
anonymous
  • anonymous
that's the answer, and I don't understand how to do that!

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anonymous
  • anonymous
PLEASE @Emeyluv99 ?
anonymous
  • anonymous
factorize the top and the bottom separately first
anonymous
  • anonymous
you mean =0?
anonymous
  • anonymous
yes
anonymous
  • anonymous
so we get (x+3)((x-6) for the nominator
anonymous
  • anonymous
and for the denominator we get (x-7)(x+2)
anonymous
  • anonymous
ok, now, what values of x cannot work
anonymous
  • anonymous
\[\frac{ (x-6)(x+3) }{ (x-7)(x+2) }\]
anonymous
  • anonymous
7 and 2
anonymous
  • anonymous
right?
anonymous
  • anonymous
but how from here?
anonymous
  • anonymous
can you please show how to calculate from here?
anonymous
  • anonymous
@Emeyluv99
anonymous
  • anonymous
sorru. computers being mean.. and be careful, its 7 and -2
anonymous
  • anonymous
now the way I would do it, graph the quadratic you get in the numerator. See what values of x give a positive y and that's you're answer. Be careful to exclude 7 and -2 though
anonymous
  • anonymous
that's what I did but I didn't get the asnswer
anonymous
  • anonymous
from graphing you should get x<-3 and x>6... but, since we can't have 7 you should get X<-3, 67
anonymous
  • anonymous
but that's not the answer... thanks though
anonymous
  • anonymous
@ganeshie8 will you be savior?
anonymous
  • anonymous
my
ganeshie8
  • ganeshie8
|dw:1440157290238:dw|
ganeshie8
  • ganeshie8
pick any number to the left of -3 say -4 plug x = -4 in the given inequality
ganeshie8
  • ganeshie8
\[\frac{ (x-6)(x+3) }{ (x-7)(x+2)}\] plugging x=-4 gives \[\frac{ (-4-6)(-4+3) }{ (-4-7)(-4+2) }\] looks it is positive, yes ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
but why would you put -4 from the first place?
anonymous
  • anonymous
?
ganeshie8
  • ganeshie8
you can put any number to the left of -3 for testing since -4 is easy to work..
anonymous
  • anonymous
oh ok, then what am I doing from here?
ganeshie8
  • ganeshie8
since a number to the left of -3 satisfies the inequality, \(x\lt 3\) is part of the solution : |dw:1440158449273:dw|
ganeshie8
  • ganeshie8
lets check the next interval \((-3, -2)\) pick a number between -3 and -2
ganeshie8
  • ganeshie8
thr ? @Hipocampus
anonymous
  • anonymous
-2.5
anonymous
  • anonymous
sorry there's a slightly problem with the internet
anonymous
  • anonymous
sorry I'm not following thanks though
anonymous
  • anonymous
it's supposed to be a really easy question
ganeshie8
  • ganeshie8
\[\frac{ (x-6)(x+3) }{ (x-7)(x+2)}\] plugging x=-2.5 gives \[\frac{ (-2.5-6)(-2.5+3) }{ (-2.5-7)(-2.5+2) }\] looks it is negative, yes ?
anonymous
  • anonymous
yes
ganeshie8
  • ganeshie8
so the interval (-3, -2) is not a solution : |dw:1440159462256:dw|
ganeshie8
  • ganeshie8
to test the next interval \((-2,6)\) pick some easy number between them and plug it in the inequality
anonymous
  • anonymous
so I need to plug in 4 times?
anonymous
  • anonymous
can we try -1.5 together please? I think I've got it!
ganeshie8
  • ganeshie8
try some easy number like x=0
ganeshie8
  • ganeshie8
0 is between -2 and 6
ganeshie8
  • ganeshie8
\[\frac{ (x-6)(x+3) }{ (x-7)(x+2)}\] plugging x=0 gives \[\frac{ (0-6)(0+3) }{ (0-7)(0+2) }\] looks it is positive, yes ?
anonymous
  • anonymous
YES!!
anonymous
  • anonymous
so between -2 and 6 it's ok
anonymous
  • anonymous
8 is negative then no
anonymous
  • anonymous
and 7.5 is fine likewise
anonymous
  • anonymous
so what we get is that -3>x, -27
anonymous
  • anonymous
you're brilliant! thank you so so much!!!!!!
anonymous
  • anonymous
7.5 isn't good right
ganeshie8
  • ganeshie8
|dw:1440159894339:dw|
ganeshie8
  • ganeshie8
double check with wolfram http://www.wolframalpha.com/input/?i=solve+%28x%5E2-3x-18%29%2F%28x%5E2-5x-14%29%3E%3D0
anonymous
  • anonymous
thanks a lot!!!!!
ganeshie8
  • ganeshie8
np, the basic procedure for solving rational inequalities is : 1) factor both numerator and denomiantor 2) find the x values where the numerator or denominator equal 0 3) plot them on number line 4) pick a number in each interval and test the inequality
anonymous
  • anonymous
@ganeshie8 is there any easier way to solve it?
ganeshie8
  • ganeshie8
hmm i can't think of any other easy way to solve it.. post it again and see what others have to say..

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