2 ≤ |x-6| < 5
Break that into two inequalities:
2 ≤ x-6 < 5 2 ≤ -(x-6) < 5
+6 +6 +6 2 ≤ -x+6 < 5
------------ -6 -6 -6
8 ≤ x < 11 -4 ≤ -x <-1
4 ≥ x > 1
You might want to write the second one in reverse so it
will go left to right instead or right to left 1 < x ≤ 4
8 ≤ x < 11, 1 < x ≤ 4
1 < x ≤ 4, 8 ≤ x < 11
----------○========●-----------○========●---------
-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Interval notation: (1,4] U (8,11]
Edwin
