Mathematics

Problem

11. A solution is to be kept between

68^{\circ} \mathrm{F}

and

77^{\circ} \mathrm{F}

. What is the range in temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by

\mathrm{F}=\frac{9}{5} \mathrm{C}+32 ?

Intuitive explanation

This is about converting a compound inequality from Fahrenheit to Celsius using an algebraic formula. You need to isolate $C$ by treating the entire inequality $68 < F < 77$ as a single statement, then apply the inverse of the conversion formula to all three parts. The key insight is that multiplying or dividing an inequality by a positive number preserves the direction of the inequality signs, so you can safely rearrange without flipping anything unexpectedly.

Intuitive explanation

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