## Intermediate Algebra (12th Edition)

$x=48$
$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $\sqrt{x+1}=7 ,$ square both sides of the equation and then isolate the variable. Then, 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( \sqrt{x+1} \right)^2=(7)^2 \\\\ x+1=49 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} x=49-1 \\\\ x=48 .\end{array} Upon checking, $x=48$ satisfies the original equation.