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 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set - Page 95: 105


a contradiction

Work Step by Step

Using the order of operations and the properties of equality, the solution to the given equation, $ -2[3(x-2)+4]=4(5-x)-2x $, is \begin{array}{l} -2[3x-6+4]=20-4x-2x \\\\ -2[3x-2]=20-6x \\\\ -6x+4=20-6x \\\\ -6x+6x=20-4 \\\\ 0=16 \text{ (FALSE)} .\end{array} Since the solution above ended with a FALSE statement, then the given equation is $\text{ a contradiction }$.
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