Question 147379
Essentially what we want here is
x < 6 or x > 11

Look at the endpoints. 6 and 11 are 5 units apart. Half of 5 is 2.5. So you want to adjust the inequality so it relates to –2.5 and 2.5 INSTEAD of 6 and 11. You will need to subtract 8.5 all around.

x-8.5 < 6-8.5  or  x-8.5 > 11-8.5
x-8.5 < -2.5  or x-8.5 > 2.5


Now, recall GOLA. This is a simple rule that says if the absolute valued terms are greater, we will use OR. If the absolute valued terms are less, we will use and.
Since this is the "greater than" format (use of or), the absolute-value inequality will be of the form "absolute value of something is greater than 2.5". You can convert this nicely to

|x-8.5| > 2.5