Question

the set of all integers x such that |x-3|<2is equal to​

Answer 1

Step-by-step explanation:

∣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

therefore (a) and (b) are not correct

x=−4⇒∣x−3∣=∣−4−3∣=∣−∣=7



<2

∴ (d) is not correct.

∴ The correct answer is (A)