Question

Find the solution of the inequation 0 < |x-3| $\le$ 1 contains the interval.

• A. x ∈ [-2, 4]
• B. x ∈ (2, 4)
• C. x ∈ [2, 4]
• D. x ∈ (-2, 4)

Answer 1

The correct option is A

x ∈ [-2, 4]

0 < |x-3| $\le$ 1

|x-3| is always positive, it can reverse less than zero. Minimum value x - 3 can take -1

-1 $\le$ x - 3 $\le$ 1

-2 $\le$ x $\le$ 4

Above inequality contains the interval

x ∈ [-2, 4]