Question

A company ordered 6-foot long oak boards. The length (l) of the boards that the company received varies from a maximum length of 0.05 inches longer than 6 feet to a minimum length of 0.05 inches shorter than 6 feet. Write and solve an absolute value inequality to represent the possible length (l) of each board in inches.

f(x)=∣9/8 (x−8)∣

Answer 1

Absolute value equation is:

|L - 72| ≤ 0.05

Solution is 71.05 ≤ L ≤ 72.5

Explanation:

We are told that the length (l) of the boards that the company received varies from a maximum length of 0.05 inches longer than 6 feet to a minimum length of 0.05 inches shorter than 6 feet.

From conversions, 1 ft gives 12 inches. Thus, converting the 6 ft to inches gives us; 6 × 12 = 72 inches

This means that minimum value of L is 72 - 0.05 and maximum is 72 + 0.05.

Thus,the absolute value equation is;

|L - 72| ≤ 0.05

Solving this gives;

L - 72 ≤ 0.05 and -(L - 72) ≤ 0.05

This gives;

L ≤ 72 + 0.05 and -L + 72 ≤ 0.05

L ≤ 72.05 and 72 - 0.5 ≤ L

L ≤ 72.05 and 71.05 ≤ L