A solution is to be kept between 68°F and 77°F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by \(F = \frac{9}{5}C + 32\,\, ?\)
Solution and Explanation
Since the solution is to be kept between 68°F and 77°F, 68 < F < 77
Putting \(F = \frac{9}{5} C + 32\) we obtain
\(68 < \frac{9}{5}C+32 < 77\)
\(⇒ 68-32 < \frac{9}{5}C + 32 < 77-32\)
\(⇒ 36 < \frac{9}{5}C < 45\)
\(⇒ 36x\frac{5}{9} < C < 45x\frac{5}{9}\)
⇒ 20 < C < 25
Thus, the required range of temperature in degree Celsius is between 20°C and 25°C.
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Concepts Used:
Inequalities
In mathematics, inequality is a relationship that compares two numbers or other mathematical expressions in a non-equal fashion. It is most commonly used to compare the size of two numbers on a number line.
Specifically, a linear inequality is a mathematical inequality that integrates a linear function. One of the symbols of inequality is observed in a linear inequality: In graph form, it represents data that is not equal.
Some of the linear inequality symbols are given below:
- < less than
- > greater than
- ≤ less than or equal to
- ≥ greater than or equal to
- ≠ not equal to
- = equal to
Inequalities can be demonstrated as questions that are solved using alike procedures to equations, or as statements of fact in the form of theorems. It is used to contrast numbers and find the range or ranges of values that pleases a variable's criteria.