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# crucial points

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VP
Status: There is always something new !!
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Joined: 08 May 2009
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16 Jul 2009, 05:56
1. To solve which kind of inequalities determining crucial point becomes neccessary.
2.In this equation how to determine the crucial point (point at which the sign changes)?
|2x +3|> x +6.

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Kudos [?]: 281 [0], given: 10

Senior Manager
Joined: 23 Jun 2009
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Kudos [?]: 134 [0], given: 80

Location: Turkey
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17 Jul 2009, 07:08
Most important point is the roots of this equation in absolute value brackets.
For this|2x +3| root is -3/2 (-3/2.2 + 3 =0)
So -3/2 is a crucial point. When x is less than this value, value in the bracket becomes negative and vice versa

Kudos [?]: 134 [0], given: 80

Manager
Joined: 27 Jun 2008
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22 Jul 2009, 23:59
Can you please elaborate how to use this information.

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SVP
Joined: 05 Jul 2006
Posts: 1750

Kudos [?]: 430 [0], given: 49

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10 Aug 2009, 00:57
[quote="amit2k9"]1. To solve which kind of inequalities determining crucial point becomes neccessary.
2.In this equation how to determine the crucial point (point at which the sign changes)?
|2x +3|> x +6.

2x+3>x+6

x>3

or

2x+3<-x-6 ie: 3x<-9 ie: x<-3 ie: the inquality is not defined in the range -3 to 3 and any other number satisfy it

draw a number line and see the

-4.....-3.....-2.....-1.....0.....1.....2.....3......4

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Director
Joined: 01 Feb 2011
Posts: 726

Kudos [?]: 143 [0], given: 42

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03 Apr 2011, 13:33
2x+3>x+6
=> x>3

-(2x+3)>(X+6)
=> x<-3

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SVP
Joined: 16 Nov 2010
Posts: 1598

Kudos [?]: 592 [0], given: 36

Location: United States (IN)
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03 Apr 2011, 18:18
so 2x +3 > -x - 6 OR 2x +3> x +6.

=> 3x > -9 OR x > 3

=> x < -3 OR x > 3
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Kudos [?]: 592 [0], given: 36

Manager
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Kudos [?]: 17 [0], given: 314

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24 Sep 2015, 10:24
in this case, crucial points are 3 and -3. and to decide what is the range just put the values -10, 10 and 0. n u will notice that this inequality is satisfied only when x >0 or x< - 3. just putting -10, 0 n 10 in the orginal eq, this range can be verified.

Kudos [?]: 17 [0], given: 314

Re: crucial points   [#permalink] 24 Sep 2015, 10:24
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