## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 7 - Section 7.6 - Solving Equations with Radicals - 7.6 Exercises: 37

#### Answer

$x=1$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $\sqrt[3]{2x+5}=\sqrt[3]{6x+1} ,$ raise both sides of the equation to the third power. Then use properties of equality to isolate and solve the variable. Finally, do checking of the solution/s with the original equation. $\bf{\text{Solution Details:}}$ Raising both sides of the equation to the third power results to \begin{array}{l}\require{cancel} \left(\sqrt[3]{2x+5}\right)^3=\left(\sqrt[3]{6x+1}\right)^3 \\\\ 2x+5=6x+1 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 2x-6x=1-5 \\\\ -4x=-4 \\\\ x=\dfrac{-4}{-4} \\\\ x=1 .\end{array} Upon checking, $x=1$ satisfies the original equation.

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