Any help?
A furniture maker uses the specification 19.88≤w≤20.12 for the width w in inches of a desk drawer. Write the specification as an absolute value inequality.

Question

Any help?
A furniture maker uses the specification 19.88≤w≤20.12 for the width w in inches of a desk drawer. Write the specification as an absolute value inequality.

austinl · Answer

One way to find the answer is to try widths that are just above and just below the maximum and minimum widths that are allowed by the specification. For example if we try a width of 20.20 (which is too long to meet the specification) in the first choice of answer we get:

|20.20−0.24|=|19.96|=19.96≤20.12

Obviously the first choice is not correct, the reason being it allows a length that is outside the specification. Can you try the values of 19.80 and 20.20 in the second choice and post the results?

anonymous · Answer

where did .24 come from?

austinl · Answer

20.12-19.88=0.24

anonymous · Answer

ohhh right, okay

austinl · Answer

Excuse me, I messed up. This was posted from another site that I help on. It had answer choices.

|w – 0.24| ≤ 20.12 
|w – 20| ≤ 0.12 
|w – 20| ≤ 0.24 
|w – 0.12| ≤ 20

anonymous · Answer

yeah, those are the same answer choices i have too...

anonymous · Answer

So, where do I plug in 20.20 and 19.80 in?

austinl · Answer

Anywho, we tried the first choice and it didn't work. Lets try the second choice.

Put 19.80 and then 20.20 instead of w in the second choice:
|19.80−20|=?
|20.20−20|=?

anonymous · Answer

|19.80-20|=-0.2
|20.20-20|= 0.2

anonymous · Answer

bu the first one can't work since it's a negative, right?

anonymous · Answer

but*

austinl · Answer

Absolute value makes any answer positive.
|19.80-20|=0.2

anonymous · Answer

oh, okay that makes sense...

austinl · Answer

Both equal 0.20. Therefore the second choice looks good, so far, the reason being that widths that are outside the specification are correctly rejected. Now try values that only just meet the specification as follows:

|19.88−20|=?
|20.12−20|=?

anonymous · Answer

both equal 0.12, right?

austinl · Answer

Both the upper and lower limits of widths the meet the specification are accepted. Also as we found previously widths that are just outside the specification are rejected. Therefore the second choice

|w−20|≤0.12

is the correct answer.

anonymous · Answer

wow, okay thanks. Sorry if I'm bothering you with all my questions..but i really appreciate it :)

austinl · Answer

Nope, no bother. Glad to help!

anonymous · Answer

Thanks!