Question

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

Answer 1

∣x−3∣ < 2 =>

3 - 2 < x < 3 + 2⇒1 < x < 5⇒x =>2,3,4.

∴ Required set => ( 1, 2, 3, 4, 5 ) or [ 2, 3, 4].

Alternative method =>

x = 1 => ∣x−3∣ = ∣1−3∣ = ∣−2∣ = 2 ≠ 2.

( 1, 2, 3, 4, 5 ) or [ 2, 3, 4] are not correct.

x = −4 ⇒ ∣x−3∣ = ∣−4−3∣ = ∣−∣ = 7 ≠ 2.

∴ ( - 4, - 3, - 2) is not correct.

∴ So, the correct answer is ( 1, 2, 3, 4, 5 ).

∴ Therefore, The set of all integers 'x' such that |x-3| <2 is equal to ( 1, 2, 3, 4, 5 ).