Question

||x-1|-2|=|x-3|
Solve the above equation for x:

Answer 1

Given : function is .. ||x - 1| - 2| = |x - 3|

To find : find the value of x.

solution : case 1 : x ≤ - 1

⇒-[-(x - 1) - 2] = -(x - 3)

⇒-x + 1 - 2 = x - 3

⇒-x - 1 = x - 3

⇒2x = 2

⇒x = 1

but x ≤ -1 , so, x ≠ -1

case 2 : -1 < x ≤ 1

⇒-[-(x - 1) - 2] = -(x - 3)

⇒-x + 1 - 2 = x - 3

⇒-x - 1 = x - 3

⇒2x = 2

⇒x = 1 [ it is a solution ]

case 3 : 1 < x ≤ 3

⇒-(x - 1 - 2) = -(x - 3)

⇒(x - 3) = (x - 3) for all real value of x.

so, x ∈ (1, 3]

case 4 : x > 3

⇒(x - 1 - 2) = (x - 3)

⇒(x - 3) = (x -3) for all real value of x.

so, x ∈ (3, ∞)

so, solution is, x ∈ {1} U (1, 3] U (3,∞) ⇒x ∈ [1, ∞)

Therefore solution of given function is x ∈ [1, ∞)

Answer 2

(1, infinity)

Step-by-step explanation:

so value of x is (1, infinity)