Grade 12Differential Calculus

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

Chilukuri Sai Kartik

16 Years agoGrade 12

2 Answers

Badiuddin askIITians.ismu Expert

16 Years ago

Dear chilukuri

||x-2|-1|>3

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

5 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, ∞)