## Intermediate Algebra (12th Edition)

$x=17$
$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $3\sqrt{x-1}=2\sqrt{2x+2} ,$ square both sides of the equation and then isolate the variable. Finally, do checking of the solution with the original equation. $\bf{\text{Solution Details:}}$ Squaring both sides of the equation results to \begin{array}{l}\require{cancel} \left( 3\sqrt{x-1} \right)^2=\left( 2\sqrt{2x+2} \right)^2 \\\\ 9(x-1)=4(2x+2) .\end{array} Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 9(x)+9(-1)=4(2x)+4(2) \\\\ 9x-9=8x+8 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 9x-8x=8+9 \\\\ x=17 .\end{array} Upon checking, $x=17$ satisfies the original equation.