Question

The lenght of a cut board in a sawmill should be within 2% of the board's official lenght. Write an absolute value inequality that describes the lenght L of an acceptable board with an official lenght of 12 feet.

Answer 1

The length L of an acceptable board must satisfy the absolute value inequality |L - 12| <= 0.24, where L is the length of the board and 0.24 feet represents 2% of the official 12-foot length.

Step-by-step explanation:

The student is asking for an absolute value inequality to determine the length L of an acceptable board in a sawmill, given that the official length is 12 feet and the board's length should be within 2% of this official length. To find the range of acceptable lengths, we can calculate 2% of 12 feet, which is 0.24 feet. Therefore, the length L of an acceptable board must satisfy the following inequality:

|L - 12| ≤ 0.24

This inequality means that the actual length L of the board must be within 0.24 feet shorter or longer than the official length of 12 feet, thus reflecting the 2% tolerance given in the problem statement.