AlgebraMediumCompound inequality through a conversion formula
Algebra practice question
The Fahrenheit temperature F of a room must satisfy 68 ≤ F ≤ 86, where F = 1.8C + 32 and C is the temperature in degrees Celsius. Which inequality gives all allowed values of C?
- A. 20 ≤ C ≤ 30Correct
- B. 36 ≤ C ≤ 54
- C. 20 < C < 30
- D. 37.8 ≤ C ≤ 47.8
Answer: A. 20 ≤ C ≤ 30
68 ≤ 1.8C + 32 ≤ 86 → 36 ≤ 1.8C ≤ 54 → 20 ≤ C ≤ 30.
Why the other answers are wrong
- B. 36 ≤ C ≤ 54
- Those are the bounds before dividing by 1.8.
- C. 20 < C < 30
- The endpoints are included.
- D. 37.8 ≤ C ≤ 47.8
- Those come from dividing by 1.8 without first subtracting 32.
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