Answer
$x=7$
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.