Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.6 - Radical Equations and Problem Solving - Exercise Set - Page 729: 31



Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ \sqrt{3x+4}=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 $ 2 $ (the same index as the radical). This results to \begin{array}{l}\require{cancel} (\sqrt{3x+4})^2=5^2 \\\\ 3x+4=25 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 3x=25-4 \\\\ 3x=21 \\\\ x=\dfrac{21}{3} \\\\ x=7 .\end{array} Upon checking, $ x=7 $ satisfies the original equation.
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