Final answer:
To find the range of acceptable tire diameters for an aircraft tire with an ideal diameter of 105 inches and an acceptable error of 0.175 inches, we use an absolute value inequality represented by |D - 105| ≤ 0.175. Solving this, we find that the acceptable diameters range from 104.825 to 105.175 inches.
Step-by-step explanation:
The question is asking for the range of acceptable tire diameters for an aircraft tire where the ideal diameter is 105 inches, with an acceptable error of 0.175 inches.
To represent this situation with an absolute value inequality, we can express it as follows:
|D - 105| ≤ 0.175,
where D represents the diameter of the tire. The inequality states that the distance between the actual diameter and the ideal diameter should be less than or equal to 0.175 inches. Solving the inequality:
- -0.175 ≤ D - 105 ≤ 0.175
- Add 105 to all parts: 104.825 ≤ D ≤ 105.175
Thus, the range of acceptable tire diameters is from 104.825 inches to 105.175 inches.