Question

12. a) Solve the following|x-1|<2. ​

Answer 1

Answer: -1 < x < 3

Work Shown:

| x-1 | < 2

-2 < x-1 < 2 ... see note1 below

-2+1 < x-1+1 < 2+1 ... see note2

-1 < x < 3

• Note1: use the rule that |x| < k turns into -k < x < k for some positive real number k.
• Note2: Add 1 to all sides to isolate x