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Question

If |x+5|10, then 
  1. x(15,5] 
  2. x(5,5] 
  3. x(,15]  [5,)  
  4. x[,15)  (5,) 


Solution

The correct option is C x(,15]  [5,)  
|x+5|10   (A)
Case 1:  x+5<0, i.e. x<5 
Then, |x+5|=x5
Then, (A) becomes x510
x15 
But x<5 x15
x(,15]   (i)

Case 2:  x+50, i.e. x5 
Then, |x+5|=x+5
Then, (A) becomes x+510
x5 
But x5 x5
x[5,)   (ii)

From (i) and (ii)
x(,15]  [5,)

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