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crucial points [#permalink]

16 Jul 2009, 05:56

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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]

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

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Re: crucial points [#permalink]

22 Jul 2009, 23:59

Can you please elaborate how to use this information.

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Re: crucial points [#permalink]

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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Re: crucial points [#permalink]

03 Apr 2011, 13:33

2x+3>x+6
=> x>3

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

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Re: crucial points [#permalink]

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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