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