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: 40

Answer

$4a$

Work Step by Step

When a grouping symbol is preceeded by a minus sign, removing the grouping symbol implies reversing the sign of all the terms inside the grouping symbol. Hence, the given expression, $ a-\{3a-[4a-(2a-4a)]\} ,$ is equivalent to \begin{array}{l}\require{cancel} a-\{3a-[4a-(2a-4a)]\} \\\\= a-\{3a-[4a-2a+4a]\} \\\\= a-\{3a-4a+2a-4a\} \\\\= a-3a+4a-2a+4a .\end{array} Carrying the subtraction and addition operators from left to right, the expression above simplifies to \begin{array}{l}\require{cancel} a-3a+4a-2a+4a \\\\= -2a+4a-2a+4a \\\\= 2a-2a+4a \\\\= 0+4a \\\\= 4a .\end{array}
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