Problem: The set of x-values satisfying the inequality 2⩽∣x−1∣⩽5 is:
Answer Choices:
A. −4⩽x⩽−1 or 3⩽x⩽6
B. 3⩽x⩽6 or −6⩽x⩽−3
C. x⩽−1 or x⩾−3
D. −1⩽x⩽3
E. −4⩽x⩽6
Solution:
The inequality 2⩽∣x−1∣⩽5 means that, when x−1 is positive, then x−1⩽5 and x−1⩾2, and that, when x−1 is negative, then x−1⩾−5 and x−1⩽−2.
Solve each of these four inequalities.
x⩽6 and x⩾3 or 3⩽x⩽6, and
x⩾4 and x⩽−1 or −4⩽x⩽−1