Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.6 - Solving Equations with Radicals - 7.6 Exercises: 2

Answer

a) Yes b) Yes

Work Step by Step

$\bf{\text{Solution Outline:}}$ Substitute the given value for $x$ in the given equation, $ \sqrt{3x-3}-x+1=0 .$ If the left side of the equation becomes equal to the right side of the equation, then the given value of $x$ is a solution to the equation. $\bf{\text{Solution Details:}}$ a) Substituting $x$ with $ 1 ,$ in the given equation results to \begin{array}{l}\require{cancel} \sqrt{3(1)-3}-1+1=0 \\\\ \sqrt{3-3}+0=0 \\\\ \sqrt{0}=0 \\\\ 0=0 \text{ (TRUE)} .\end{array} Hence, $x= 0 $ is a solution to the given equation. b) Substituting $x$ with $ 4 ,$ in the given equation results to \begin{array}{l}\require{cancel} \sqrt{3(4)-3}-4+1=0 \\\\ \sqrt{12-3}-3=0 \\\\ \sqrt{9}-3=0 \\\\ 3-3=0 \\\\ 0=0 \text{ (TRUE)} .\end{array} Hence, $x= 4 $ is a solution to the given equation.
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