Afurniture maker uses the specification 21.88 (< =) w (< =)22.12 for the width w in inches of a desk drawer. write the specification as an absolute value inequality.
a) |w- 0.24|(< =) 22.12
b) |w- 22 |(< =) 0.24
c) |w- 0.12| (< =) 22
d) |w- 22| (< =) 0.12
its not a

For C, we can subtract 0.12 from 21.88 and 22.12 (and make them an absolute value) to get |21.76|≤|w-0.12|≤|22|, which isn't true as 21.76 <22

For B, we can plug it in similarly to get |21.88-22|≤|w-22|≤|22.12-22|=
|-0.12|≤|w-22|≤|0.12|. As making the absolute value of -0.12 into 0.12 would involve multiplying it by something negative, that turns it into 
0.12≥|w-22|≤0.12 by switching the sign around. However, this perfectly fits for D, which is therefore correct!