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by anshumishra » Tue Dec 28, 2010 5:33 pm
jsasipriya wrote:|y|>|y+1|

Please explain how to simplify the above inequality.
|y| > |y+1|

This means distance of y from 0 is greater than distance of y from -1
=> y < -1/2 (As any point left of -1/2 on the number line will be close to -1 and far from 0).
Last edited by anshumishra on Tue Dec 28, 2010 9:10 pm, edited 1 time in total.
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by anshumishra » Tue Dec 28, 2010 5:47 pm
jsasipriya wrote:|y|>|y+1|

Please explain how to simplify the above inequality.
Algebraic approach :

|y| > |y+1|
if y> 0
=> y > y+1 which has no solution.

if y< -1; then |y| > |y+1| reduces to
-y > -y -1; which is true for all y. So; y> -1

Now, if -1<y<0, then |y| > |y+1| reduces to
-y > y+1
=> 2y < -1
=> y< -1/2; So, -1<y<-1/2

Combining the two solution we get : y< -1/2
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