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Inequalities

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Manager
Joined: 29 Dec 2014
Posts: 81

Kudos [?]: 2 [0], given: 997

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09 Mar 2016, 18:56
Hi, i came across the below in someone's notes. Please could you help me understand the same:

If d is NEGATIVE and |x| < d, then there is no solution
If d is NEGATIVE and |x| > d, then x is all real numbers

Thanks.

Kudos [?]: 2 [0], given: 997

Math Expert
Joined: 02 Aug 2009
Posts: 5227

Kudos [?]: 5877 [1], given: 118

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09 Mar 2016, 19:06
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Expert's post
WilDThiNg wrote:
Hi, i came across the below in someone's notes. Please could you help me understand the same:

If d is NEGATIVE and |x| < d, then there is no solution
If d is NEGATIVE and |x| > d, then x is all real numbers

Thanks.

Hi,
lets see the two statements one by one--
1)If d is NEGATIVE and |x| < d, then there is no solution
this tells us that d is NEGATIVE, BUT the value |x| cannot be NEGATIVE...
the mininmum |x| will be 0 when x=0,
if x=-2,-3 etc, |x|=2,3..
so there are no values of x that can fit in here

2)If d is NEGATIVE and |x| > d, then x is all real numbers
same as above..
if d is -IVE, any value of x will have a modulus|x| as +ive and will always be greater than d..

|x| means the distance of x from 0 on the number line ..
|x| is always positive or 0..

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5877 [1], given: 118

Manager
Joined: 29 Dec 2014
Posts: 81

Kudos [?]: 2 [0], given: 997

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09 Mar 2016, 19:38
Got it - many thanks

Kudos [?]: 2 [0], given: 997

Re: Inequalities   [#permalink] 09 Mar 2016, 19:38
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