Question

Which of the following expressions is equivalent to |x – 2| < 3?
A.

–3 > x – 2 < 3
B.

–3 < x – 2 < 3
C.

x – 2 < 3 and x – 2 < –3
D.

x – 2 < 3 or x – 2 < –3

Answer 1

the correct answer is B....you know how it is solved??

Answer 2

not really. this has been pretty hard for me

Answer 3

look why it is option B...i'll explain...
when x-2 is greater than -3, i.e., -3<x-2, then x-2 has any values starting from -2.999..
so modulus of x-2 will always be less than 3.
again when it'll be less than 3, i.e., x-2<3, then all values of x-2 will be less than 3. so mod x-2 will always be less than 3 within -3 and 3.

Answer 4

ok that actually helped, thank you at first i didnt get it. thanks man