Question

Solve the inequality |X| -1 / |X|-2 >=0, X belongs to R and X not equal to +-2

Answer 1

Answer:

X < - 2  ,   -1 ≤ X ≤ 1 ,   X > 2

Step-by-step explanation:

|X| - 1 / |X| - 2  >= 0

|X| - 1 = 0

or |X| - 1   &  |X| - 2 > 0

or if  |X| - 1   &  |X| - 2 < 0

Case 1  : |X| - 1 = 0

=> |X| = 1

=> X = ± 1

Case 2 :

|X| - 1   &  |X| - 2 > 0

=>  |X| - 1 > 0    =>  |X|  > 1   =>  X > 1  or X < - 1

also  |X| - 2 > 0 =>  |X|  > 2   =>  X > 2  or X < - 2

from Both     X > 2  or X < - 2

Case 3 :

|X| - 1   &  |X| - 2 < 0

=>   |X| - 1 < 0    =>  |X|  < 1   =>  X < 1  & X > - 1 = >  -1 < X < 1

=>   |X| - 2 < 0    =>  |X|  < 2   =>  X < 2 &  X > - 2 = >  -2 < X < 2

from Both  -1 < X < 1

also X = ± 1

so  -1 ≤ X ≤ 1

Hence  X < - 2  ,   -1 ≤ X ≤ 1 ,   X > 2