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  4. The set of all real x satisfying the in equal (3-|x|/4-|x|) ge 0

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Q. The set of all real $ x $ satisfying the in equal $ \frac{3-|x|}{4-|x|}\ge 0 $

KEAMKEAM 2009Linear Inequalities

Solution:

Given, $ \frac{3-|x|}{4-|x|}\ge 0 $
$ \Rightarrow $ $ 3-|x|\le 0 $ and $ 4-|x|<0 $ Or $ 3-|x|\ge 0 $ and $ 4-|x|>0 $
$ \Rightarrow $ $ |x|\ge 3 $ and $ |x|>4 $ Or $ |x|\le 3 $ and $ |x|<4 $
$ \Rightarrow $ $ |x|>4 $ or $ |x|\le 3 $
$ \Rightarrow $ $ (-\infty ,-4)\cup [-3,3]\cup (4,\infty ) $