the length of a cut board in a sawmill should be within 2% of the board's stated length.write an absolute value inequality that describes the length L of an acceptable board with a stated length of 12 feet.
To create an absolute value inequality that describes the acceptable length (L) of a board with a stated length of 12 feet, we need to consider that the length should be within 2% of the stated length.
The range within 2% of the stated length can be calculated by finding 2% of the stated length and subtracting it from the stated length to get the lower bound, and adding it to the stated length to get the upper bound.
2% of 12 feet is calculated as (2/100) * 12 = 0.24 feet.
The lower bound is found by subtracting 0.24 feet from the stated length: 12 - 0.24 = 11.76 feet.
The upper bound is found by adding 0.24 feet to the stated length: 12 + 0.24 = 12.24 feet.
So, the acceptable length of a board can be expressed using an absolute value inequality:
|L - 12| ≤ 0.24
This inequality states that the absolute value of the difference between the length of the board (L) and 12 must be less than or equal to 0.24 feet.