## Intermediate Algebra (6th Edition)

Published by Pearson

# Chapter 7 - Section 7.6 - Radical Equations and Problem Solving - Exercise Set: 30

#### Answer

$x=45$

#### Work Step by Step

Using the properties of equality, the given equation, $\sqrt[4]{2x-9}-3=0 ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[4]{2x-9}=3 .\end{array} Raising both sides of the equation above to the fourth power, then the solution/s is/are \begin{array}{l}\require{cancel} 2x-9=81 \\\\ 2x=81+9 \\\\ 2x=90 \\\\ x=\dfrac{90}{2} \\\\ x=45 .\end{array} Upon checking, $x=45$ satisfies the original equation.

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