Question

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

• A. $(1,2,3,4,5)$
• B. $(1,2,3,4)$
• C. $(2,3,4)$
• D. $(-4,-3,-2)$

Answer 1

The correct option is A $(1,2,3,4,5)$

$|x-3|<2\Rightarrow 3-2<x<3+2\Rightarrow 1<x<5$
$\Rightarrow x=2,3,4$.
$\therefore$ Required set $=(1,2,3,4,5)or[2,3,4]$.

Alternative method
$x=1\Rightarrow |x-3|=|1-3|=|-2|=2\nless 2$
$therefore$ (a) and (b) are not correct
$x=-4\Rightarrow |x-3|=|-4-3|=|-|=7\nless 2$
$\therefore$ (d) is not correct.
$\therefore$ The correct answer is (A).