Question

If x is an integer greater than-10, but less than 10 and $|x-2|<3,$ then the values of x are

• A. $-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,$
• B. $0,1,2,3,4,5,6,7,8,9,10,$
• C. $0,1,2,3,4,$
• D. $-1,0,1$

Answer 1

The correct option is C $0,1,2,3,4,$

It is given that
$-10<x<10$
That is
$|x|<10$ ...(i)
Now
$|x-2|<3$
$-3<x-2<3$
$-1<x<5$ ...(ii)
Hence
from ii,
$xϵ(-1,5)$ and from i $xϵ(-10,10)$
Hence
$xϵ(-1,5)$
Now x is an integer.
Hence the set of integers falling in the above solution set is
$\{0,1,2,3,4\}$.