Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.6 - Radical Equations and Problem Solving - Exercise Set: 46

Answer

$x=\dfrac{4}{7}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ \sqrt{7x-4}=\sqrt{4-7x} ,$ raise both sides to the exponent equal to the index of the radical. Then use the properties of equality to isolate the variable. Finally, do checking of the solution/s with the original equation. $\bf{\text{Solution Details:}}$ Get rid of the radical symbol by raising both sides of the equation above to the exponent equal to $ 2 $ (the same index as the radical). This results to \begin{array}{l}\require{cancel} (\sqrt{7x-4})^2=(\sqrt{4-7x})^2 \\\\ 7x-4=4-7x .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 7x+7x=4+4 \\\\ 14x=8 \\\\ x=\dfrac{8}{14} \\\\ x=\dfrac{4}{7} .\end{array} Upon checking, $ x=\dfrac{4}{7} $ satisfies the original equation.
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