The set of all integers x such that |x – 3| < 2 is equal to

|x – 3| < 2       ⇒ 3 – 2 < x < 3 + 2        ⇒ 1 < x < 5

⇒ x = 2, 3, 4

∴ Required set = {2, 3, 4}

Alternative method

x = 1 ⇒ |x – 3| = |1 – 3| = |– 2| = 2 ≮ 2

∴ (a) and (b) are not correct

x = – 4 ⇒ |x – 3| = |– 4 – 3| = |– 2| = 7 ≮ 2

∴ (D) is not correct.

Hence (3) is the correct answer.