Final answer:
The longest the piece is allowed to be is 12.01 cm, and the shortest is 11.99 cm. The range of acceptable values is 11.99 cm ≤ length ≤ 12.01 cm.
Step-by-step explanation:
The specifications state that the length of the metal piece must be 12 cm, with a tolerance of ±0.01 cm. This means that the longest the piece is allowed to be is 12 cm + 0.01 cm = 12.01 cm. On the other hand, the shortest the piece is allowed to be is 12 cm - 0.01 cm = 11.99 cm. Therefore, the range of acceptable values for the length of the piece can be expressed as the inequality 11.99 cm ≤ length ≤ 12.01 cm.