The set of all integers 'X' such that X-3|<2 is equal to
{2,3,4}
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∣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).
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