Question

the least positive integer in solution set of x in equation ||x-2|-1|>=3,is​

Answer 1

Given :  | | x - 2 |  -  1 |   ≥  3  

To Find :   least positive integer in solution set of x

Solution:

| | x - 2 |  -  1 |   ≥  3  

Case 1 :

x - 2  ≥ 0  

=> x ≥ 2

| x - 2 |  = x - 2

|  x  - 2 - 1 |   ≥  3  

| x - 3 |  ≥  3  

=> x   ≥  6     , x  <  0

so x ≥  6

Case 1

x - 2  <  0

=> x  <  2

| x - 2 |  = - (x - 2 ) = 2 - x

| 2 -x   -  1 |   ≥  3  

=> |  1  - x |  ≥  3  

=>  x  ≤  - 2

Solution :

x  ≤  - 2  and   x ≥  6  

least positive integer in solution set of x in equation = 6  

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