Final answer:
The acceptable engine temperatures range is represented by the absolute value inequality |T - 180°F| ≤ 20°F. The unacceptable temperature range for the engine is expressed by the inequality |T - 180°F| > 20°F, indicating temperatures outside the 160°F to 200°F range.
Step-by-step explanation:
The optimal operating temperature of a given car engine is within 20 degrees Fahrenheit of 180 degrees Fahrenheit. To express the range of acceptable temperatures, we can write an absolute value inequality. The absolute value of the difference between the engine's temperature (T) and the optimal temperature (180°F) must be less than or equal to 20°F:
|T - 180°F| ≤ 20°F
This means the temperature must be between 160°F and 200°F for the engine to operate optimally.
To express the range of unacceptable temperatures, we can write another absolute value inequality indicating that the temperature must not be within 20°F of 180°F:
|T - 180°F| > 20°F
This means any temperature lower than 160°F or higher than 200°F is not acceptable for the car engine's operation.