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Absolutes QUESTION - MGMAT Article

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Absolutes QUESTION - MGMAT Article  [#permalink]

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New post 30 Nov 2017, 06:49
Hello guys,

this article: https://www.manhattanprep.com/gmat/tuto ... -value.cfm talks about the critical points in absolutes.
It has this example: |x + 1| + |x - 3| = 6 where the critical points are -1 and 3 and defines the critical points as the numbers that zero | |.

Why in the inequality below the critical point is not -3? It is -6 and 0.
|x+3|>3 is equal to x e (-inf,-6)&(0,+inf)

Thanks
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Re: Absolutes QUESTION - MGMAT Article  [#permalink]

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New post 30 Nov 2017, 07:09
standyonda wrote:
Hello guys,

this article: https://www.manhattanprep.com/gmat/tuto ... -value.cfm talks about the critical points in absolutes.
It has this example: |x + 1| + |x - 3| = 6 where the critical points are -1 and 3 and defines the critical points as the numbers that zero | |.

Why in the inequality below the critical point is not -3? It is -6 and 0.
|x+3|>3 is equal to x e (-inf,-6)&(0,+inf)

Thanks



hi.

the critical point is -3 itself..
at x<-3, x+3 will be NEGATIVE, so -(x+3)>3.....x+3<-3....x<-6...lower limit -Inf
at x>=-3, x+3>3...x>0.. Higher limit +inf
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Absolutes QUESTION - MGMAT Article  [#permalink]

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New post 30 Nov 2017, 07:14
chetan2u wrote:
standyonda wrote:
Hello guys,

this article: https://www.manhattanprep.com/gmat/tuto ... -value.cfm talks about the critical points in absolutes.
It has this example: |x + 1| + |x - 3| = 6 where the critical points are -1 and 3 and defines the critical points as the numbers that zero | |.

Why in the inequality below the critical point is not -3? It is -6 and 0.
|x+3|>3 is equal to x e (-inf,-6)&(0,+inf)

Thanks



hi.

the critical point is -3 itself..
at x<-3, x+3 will be NEGATIVE, so -(x+3)>3.....x+3<-3....x<-6...lower limit -Inf
at x>=-3, x+3>3...x>0.. Higher limit +inf


Thanks!! So to find the range you use the critical point that in the end it has nothing to do with the range. The CP is a step.
GMAT Club Bot
Re: Absolutes QUESTION - MGMAT Article &nbs [#permalink] 30 Nov 2017, 07:14
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Absolutes QUESTION - MGMAT Article

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