Question

The proper height of a highway guardrail is 27 inches, but 3 inches higher or lower is acceptable. Which inequality represents the acceptable heights, h, of a highway guardrail?

A.|h+27|≤3
B.|h−3|≤27
C.|h+3|≤27
D.|h−27|≤3

Answer 1

Explanation:

27 is the "center" of a range of measurements of the height of the guard rail. The height could be as much as 30 inches or as little as 24 inches. The absolute value operator encloses "x - 27," where 27 is the "center." The acceptable excess or acceptable deficiency is 3 inches.

So now we can eliminate possible answers B and C, in both cases because 27 is inappropriately greater than 3.

Narrowing down our choices, we have h + 27 and h - 27 inside the absolute value operator. 27 is a positive quantity (height of the guard rail), so the inequality showing +27 as the "center" is correct; that is

D: |h - 27| ≤ 3 (measurements in inches).