∣x−9∣≤2
The given inequality states that the absolute value of (x - 9) is less than or equal to 2.
This means that (x - 9) can be any value between -2 and 2, inclusive.
Simplifying the inequality:
-2 ≤ (x - 9) ≤ 2
Adding 9 to all sides of the inequality:
-2 + 9 ≤ (x - 9) + 9 ≤ 2 + 9
7 ≤ x ≤ 11
Therefore, the solution to the inequality is 7 ≤ x ≤ 11.