## Algebra: A Combined Approach (4th Edition)

Published by Pearson

# Chapter 10 - Section 10.6 - Radical Equations and Problem Solving - Exercise Set - Page 729: 41

#### Answer

$x=1$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $\sqrt[3]{-6x-1}=\sqrt[3]{-2x-5} ,$ 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 $3$ (the same index as the radical). This results to \begin{array}{l}\require{cancel} (\sqrt[3]{-6x-1})^3=(\sqrt[3]{-2x-5})^3 \\\\ -6x-1=-2x-5 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} -6x+2x=-5+1 \\\\ -4x=-4 \\\\ x=\dfrac{-4}{-4} \\\\ x=1 .\end{array} Upon checking, $x=1$ satisfies the original equation.

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