Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 1 - Introduction to Algebraic Expressions - Test: Chapter 1 - Page 78: 41



Work Step by Step

If $a=1,$ $b=2,$ and $c=3,$ then the expression, $a|b-c|,$ evaluates to \begin{array}{l}\require{cancel} a|b-c|=1|2-3| \\\\ a|b-c|=1|-1| \\\\ a|b-c|=1(1) \\\\ a|b-c|=1 ,\end{array} while the expression $|ab|-|ac|$ evaluates to \begin{array}{l}\require{cancel} |ab|-|ac|=|1(2)|-|1(3)| \\\\ |ab|-|ac|=|2|-|3| \\\\ |ab|-|ac|=2-3 \\\\ |ab|-|ac|=-1 .\end{array} Hence, the given statement, $a|b-c|=|ab|-|ac|,$ is $\text{ FALSE .}$
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