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 10 - Exponents and Radicals - 10.6 Solving Radical Equations - 10.6 Exercise Set: 42

Answer

$x=\dfrac{1}{2}$

Work Step by Step

Raising both sides to the third power results to \begin{array}{l}\require{cancel} 2(1-x)^{1/3}=4^{1/3} \\\\ \left( 2(1-x)^{1/3} \right)^3=\left( 4^{1/3} \right)^3 \\\\ 8(1-x)=4 .\end{array} Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 8(1-x)=4 \\\\ 8(1)+8(-x)=4 \\\\ 8-8x=4 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 8-8x=4 \\\\ -8x=4-8 \\\\ -8x=-4 \\\\ x=\dfrac{-4}{-8} \\\\ x=\dfrac{1}{2} .\end{array}
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