Question

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.

Answer 1

The correct answer is:

|w-20| ≤ 0.12.

Explanation:

We first find the average of the two ends of the inequality:

(19.88+20.12)/2 = 40/2 = 20

This will be the number subtracted from w in the inequality.

Now we find the difference between this value and the ends:

20-19.88 = 0.12

20.12 - 20 = 0.12

This will be what our absolute value inequality ends with; the "answer" part, so to speak.

Since this inequality is written in compact form, it must be an "and" inequality; this means the absolute value inequality must be a "less than or equal to."

This gives us

|w-20| ≤ 0.12

Answer 2

A furniture maker uses the specification 19.88 ≤ w ≤ 20.12

The absolute value inequality is

$|x-20|\leq 0.12$

Given :

A furniture maker uses the specification 19.88 ≤ w ≤ 20.12 for the width w in inches of a desk drawer

We need to write the given inequality in absolute value inequality

if $a-b<x<a+b$ then absolute value inequality is

$|x-a|< b$

To find out value of 'a'  and 'b' we need to use the given inequality

compare a-b<x<a+b with given inequality

$a-b=19.88\\a+b=20.12$

Solve for 'a'  and 'b'

Add both equations

$2a=40\\a=20$

Now find out b

$a+b=20.12\\20+b=20.12\\b=20.12-20\\b=0.12$

The required absolute value inequality is

$|x-a|\leq b\\|x-20|\leq 0.12$

Learn more : brainly.com/question/1770168