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Solve ||x-2|-1| > 3

Solve ||x-2|-1|>3

Grade:12

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear chilukuri

||x-2|-1|>3

or

          3 ≤|x-2|-1        and                |x-2|-1 ≤-3

or      4 ≤|x-2|        and                     |x-2| ≤-2

1.)       4 ≤|x-2| 

        or           4 ≤(x-2)           and    x-2 ≤-4

                x>=6             and x<=-2

 

2) |x-2| ≤-2

         or         |x-2| ≤-2

           mod can't be negative so no solution

 so final solution

x>=6             and x<=-2

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Sagnik Chanda
26 Points
2 years ago
||x-2|-1|  ≥ 3
-3  ≥ |x-2| -1  ≥ 3
CASE 1 :  
|x-2| -1  ≥ 3
|x-2| ≥ 4
-4 ≥ x-2                  and              x-2 ≥ 4
-2 ≥ x                      and             x ≥ 6
∴ x ∈ (-∞, -2) ∪ (6, ∞)

 CASE 2 :
|x-2|-1  ≤ -3 
|x-2|  ≤ -2      ( which is not possible )  

∴ x ∈ (-∞, -2) ∪ (6, ∞)




 

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