Question

The circumference of a ball for a sport played by college women must be from 21.5 in. to 33.0 in. What absolute value inequality represents the circumference of the ball?​

Answer 1

The circumference of the ball must be between 21.5 inches and 33.0 inches. The absolute value inequality representing this condition is |C - 27.25| ≤ 5.75.

Step-by-step explanation:

The absolute value inequality representing the circumference of the ball is based on the condition that the circumference (C) should be no less than 21.5 inches and no more than 33.0 inches. This can be expressed as 21.5 ≤ C ≤ 33.0. To convert this to an absolute value inequality, we consider the midpoint between 21.5 and 33.0, which is 27.25. The distance from this midpoint to either extreme is 5.75 inches. Therefore, the absolute value inequality can be written as |C - 27.25| ≤ 5.75. This inequality means that the distance of the circumference from 27.25 inches must be less than or equal to 5.75 inches.