Question

Solution of set
1<=|x-2|<=3 is​

Answer 1

Answer:

-2 < |x-3| - 4 < 2

-2+4 < |x-3| < 2+4

2 < |x-3| < 6

Now, if (x-3) > 0

We will get

2 < x-3 < 6

2+3 < x < 6+3

6 < x < 9

But, if (x-3) < 0

We will get

2 < -( x-3) < 6

Which implies, -6 < x-3 < -2

-6+3 < x < -2+3

-3 < x < 1

Which implies, x belongs to (-3,1) U (6,9)