Problem: For x real, the inequality 1≤∣x−2∣≤7 is equivalent to
Answer Choices:
A. x≤1 or x≥3
B. 1≤x≤3
C. −5≤x≤9
D. −5≤x≤1 or 3≤x≤9
E. −6≤x≤1 or 3≤x≤10
Solution:
First when x−2≥0, then 1≤x−2≤7,3≤x≤9. Again when x−2≤0, then 1≤2−x≤7, −1≤−x≤5 gives −5≤x≤1 as the other possibility is stated in choice (D).