Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.5 - Compound Inequalities - Exercise Set - Page 96: 91

Answer

$\left(-\dfrac{101}{5}\right)^oF \text{ to }95^oF$

Work Step by Step

Using $C=\dfrac{5}{9}(F-32),$ then the equivalent range of Fahrenheit values for $-29^oC$ to $35^oC$ is \begin{array}{l}\require{cancel} -29\le\dfrac{5}{9}(F-32)\le35 .\end{array} Using the properties of inequality, then \begin{array}{l}\require{cancel} \dfrac{9}{5}\left( -29 \right) \le\dfrac{9}{5}\cdot\dfrac{5}{9}(F-32)\le\dfrac{9}{5}\cdot35 \\\\ -\dfrac{261}{5} \le F-32\le63 \\\\ -\dfrac{261}{5}+32 \le F-32+32\le63+32 \\\\ -\dfrac{261}{5}+\dfrac{160}{5} \le F\le95 \\\\ -\dfrac{101}{5}\le F\le95 .\end{array} Hence the equivalent range of temperature in Fahrenheit is $ \left(-\dfrac{101}{5}\right)^oF \text{ to }95^oF .$
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