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: 36

Answer

$x=-6$

Work Step by Step

Using the properties of equality, the given equation, $ \sqrt[3]{6x+9}+5=2 $, is equivalent to \begin{array}{l} \sqrt[3]{6x+9}=2-5 \\\\ \sqrt[3]{6x+9}=-3 .\end{array} Raising both sides to the $\text{ 3rd }$ power, the solution to the equation above, $ \sqrt[3]{6x+9}=-3 $, is \begin{array}{l} 6x+9=-27 \\\\ 6x=-27-9 \\\\ 6x=-36 \\\\ x=-\dfrac{36}{6} \\\\ x=-6 .\end{array}
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