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A furniture 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

Respuesta :

coolstick
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!

Answer:

Option D is correct

[tex]|w-22|\leq 0.12[/tex]

Step-by-step explanation:

If absolute value inequality is: [tex]|X-a| \leq b[/tex] then;

[tex]-b\leq X-a\leq x[/tex]            .....[1]

As per the statement:

A furniture maker uses the specification  for the width w in inches of a desk drawer.

[tex]21.88 \leq w \leq 22.12[/tex]

Subtract 22 from each side we get;

[tex]21.88-22 \leq w-22 \leq 22.12-22[/tex]

Simplify:

[tex]-0.12 \leq w-22 \leq 0.12[/tex]

From [1] we have;

[tex]|w-22|\leq 0.12[/tex]

Therefore, the specification as an absolute value inequality is , [tex]|w-22|\leq 0.12[/tex]

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