Answer: 3.45meters
Explanation:
To find the range of the length of pipe that the plumber can cut, we need to write an absolute value inequality that expresses the condition that the length of the pipe must be within 0.09 meters of the required length. Let's call the required length L.
The plumber can cut a pipe that is within 0.09 meters of the required length, so the length of the pipe must be between L - 0.09 and L + 0.09. We can express this as:
|3.36 - L| ≤ 0.09
To solve this inequality, we need to consider two cases: when 3.36 - L is positive and when it is negative.
Case 1: 3.36 - L ≥ 0
In this case, the absolute value of 3.36 - L is equal to 3.36 - L. So we can write:
3.36 - L ≤ 0.09
Solving for L, we get:
L ≥ 3.36 - 0.09
L ≥ 3.27
Therefore, if 3.36 - L is positive, the length of the pipe must be greater than or equal to 3.27 meters.
Case 2: 3.36 - L < 0
In this case, the absolute value of 3.36 - L is equal to -(3.36 - L), or L - 3.36. So we can write:
L - 3.36 ≤ 0.09
Solving for L, we get:
L ≤ 3.36 + 0.09
L ≤ 3.45
Therefore, if 3.36 - L is negative, the length of the pipe must be less than or equal to 3.45 meters.
Putting these two cases together, we get:
3.27 ≤ L ≤ 3.45
Therefore, the range of the length of pipe that the plumber can cut is between 3.27 meters and 3.45 meters.