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crucial points

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crucial points [#permalink] New post 16 Jul 2009, 04:56
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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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Re: crucial points [#permalink] New post 17 Jul 2009, 06:08
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 ;)
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Re: crucial points [#permalink] New post 22 Jul 2009, 22:59
Can you please elaborate how to use this information.
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Re: crucial points [#permalink] New post 09 Aug 2009, 23:57
[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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Re: crucial points [#permalink] New post 03 Apr 2011, 12:33
2x+3>x+6
=> x>3

-(2x+3)>(X+6)
=> x<-3
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Re: crucial points [#permalink] New post 03 Apr 2011, 17:18
so 2x +3 > -x - 6 OR 2x +3> x +6.


=> 3x > -9 OR x > 3


=> x < -3 OR x > 3
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Re: crucial points   [#permalink] 03 Apr 2011, 17:18
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