# Chapter 7 - Section 7.6 - Solving Equations with Radicals - 7.6 Exercises: 1

a) Yes b) No

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Substitute the given value for $x$ in the given equation, $\sqrt{3x+18}-x=0 .$ 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 $6 ,$ in the given equation results to \begin{array}{l}\require{cancel} \sqrt{3(6)+18}-6=0 \\\\ \sqrt{18+18}-6=0 \\\\ \sqrt{36}-6=0 \\\\ 6-6=0 \\\\ 0=0 \text{ (TRUE)} .\end{array} Hence, $x= 6$ is a solution to the given equation. b) Substituting $x$ with $-3 ,$ in the given equation results to \begin{array}{l}\require{cancel} \sqrt{3(-3)+18}-(-3)=0 \\\\ \sqrt{-9+18}+3=0 \\\\ \sqrt{9}+3=0 \\\\ 3+3=0 \\\\ 6=0 \text{ (FALSE)} .\end{array} Hence, $x= -3$ is NOT a solution to the given equation.

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