Practicing Success
The set of all integers x such that |x – 3| < 2 is equal to |
{1, 2, 3, 4, 5} {1, 2, 3, 4} {2, 3, 4} {–4, –3, –2} |
{2, 3, 4} |
|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. |