Question

Please help me with the following:

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

I know the answer isn't A because I got it wrong, but I think the answer is B. Is B correct?

Please help me by checking my answer. Any help will be appreciated! :)

Answer 1

B is correct.

|x-2| means the difference between x and 2. That difference must be less than 3, so

2-3 < x < 2+3
-3 < x-2 < 3

Answer 2

Thank you Steve!! I was stuck on this one for so long! I have such a hard time with these, so it's going to happen for me. :)