Question

| | x-3 | - 4 | < 2 then x belongs please solve this please answer i will mark them as brainlist and wrong answer will be reported​

Answer 1

Answer:

i hope you like my answer .........

Answer 2

x ∈ (-3,1) ∪ (5,9)

Given:

| | x-3 | - 4 | < 2

To Find:

The interval in which x belongs.

Solution:

We have been given that | | x-3 | - 4 | < 2

⇒ -2< |x-3|-4< 2

⇒ -2+4 < |x-3| < 2+4

⇒2 < |x-3| < 6  .............................(A)

Now (x-3)<0 or (x-3)>0

Case 1:  When (x-3)<0, equation A becomes

  2 < -(x-3) < 6

⇒-6< (x-3) < -2

⇒-6< x-3 < -2

⇒-6+3 < x< -2+3

⇒ -3< x< 1

⇒ x ∈ (-3,1)    .............................(1)

Case 2:  When (x-3)>0, equation A becomes

  2 < (x-3) < 6

⇒2 < x-3 < 6

⇒2+3 < x < 6+3

⇒ 5< x <9

⇒ x ∈ (5,9)  .............................(2)

From equation 1 and equation 2, we have

x ∈ (-3,1) and x ∈ (5,9)

⇒ x ∈ (-3,1) ∪ (5,9)

Hence  x ∈ (-3,1) ∪ (5,9)    

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