Question

The least positive integer in solution set of x in the 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  as  x ≥ 2

Case 2

x - 2  <  0

=> x  <  2

| x - 2 |  = - (x - 2 ) = 2 - x

| 2 -x   -  1 | >  3  

=> |  1  - x |  >  3  

=>  x  <  - 2   or  x > 4

 x  <  - 2   as   x  <  2  

Solution :

x  ≤  - 2  and   x ≥  6  

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

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