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## inequalities

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### inequalities

by beater » Fri Sep 05, 2008 11:47 am
If x + y + z > 0, is z > 1?

1. z > x + y + 1
2. x + y + 1 < 0

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by mals24 » Fri Sep 05, 2008 12:34 pm
Given: x+y+z>0----equ 1

St 1: z>x+y+1

adding the two equations you get: x+y+2z>x+y+1
canceling x+y from both sides you get: 2z>1--->z>0.5-----INSUFF

St 2: x+y+1<0-----equ 2
we need to change the less than sign to greater than in order to add it with equ 1
Hence multiply -1 in equ 2 which gives us---> -(x+y+1)>0
Now add this equ with equ 1 and we get ----> z-1>0
ie z>1 SUFF