Question

Charlie is making braided key chains and determined that she needs 25 centimeters of cord for each key chain. She can still make the keychain if the cord is within 2.5 centimeters. What are the ranges of cord lengths that Charlie can use to make the keychains?

Write and solve an absolute value inequality to represent this situation, where x represents the actual cord length for a keychain.

Answer 1

Charlie can use cord lengths between 22.5 centimeters and 27.5 centimeters for her keychains, calculated by the absolute value inequality |x - 25| ≤ 2.5.

Step-by-step explanation:

Charlie can use cord lengths that are within 2.5 centimeters of the desired 25 centimeters. To find the range of cord lengths, we'll create an absolute value inequality. The inequality is |x - 25| ≤ 2.5, where x represents the actual cord length.

The inequality can be interpreted as the actual cord length, x, being no more than 2.5 centimeters away from 25 centimeters, either shorter or longer. Solving the inequality:

1. x - 25 ≤ 2.5
2. x ≤ 27.5
3. -2.5 ≤ x - 25
4. -2.5 + 25 ≤ x
5. 22.5 ≤ x

Thus, Charlie can use cord lengths that are between 22.5 centimeters and 27.5 centimeters in length.