Write an absolute value to describe: 6 is at most 3 units from x

The distance from 6 to x can be written as 6-x or as x-6. We generally want the positive distance, so we can use the absolute value function to turn either one of these forms to a positive value:

|6-x| or |x-6| . . . . . . each is fully equivalent to the other

This distance is at most 3, so we can write ...

|6 -x| ≤ 3

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Comment on the form of the answer

The expression could also be written as |x-6| ≤ 3. We chose the one we did because the wording regards the distance of 6 from x. Usually the "from" value is considered the reference that is subtracted from anything we want to compare to that reference. This is a matter of convention and personal preference, not a requirement for the solution to the problem.