Question

the solution set of the inequation 3/|x|+2=<1​

Answer 1

Given :   3/(|x|+2) =< 1​

To Find :  solution set

Solution:

3/ (|x |  + 2)  ≤  1

=>   3   ≤  |x |  + 2

=>   1   ≤  |x |  

|x |    = x  if x ≥ 0

           -x  if x < 0

case 1

x ≥ 0

1   ≤  x  

Hence  x  ≥ 1

case 2

x < 0

 1   ≤  -x

=> x  ≤   -1

hence  x  ≤   -1

x  ≤   -1  ,   x  ≥ 1    

x ∈ ( -∞ , - 1] ∪ [ 1 , ∞)

solution set of the inequation 3/(|x |  + 2)  ≤  1

is x ∈ ( -∞ , - 1] ∪ [ 1 , ∞)

if its

3/|x| + 2 ≤ 1​

Then 3/|x|  ≤ -1​

3/|x|  can not be -ve

Hence no value of x

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