Answer
$x=8$
Work Step by Step
The given equation is
$\Rightarrow \sqrt{3x+1}=\sqrt{4x-7}$
Square each side of the equation.
$\Rightarrow (\sqrt{3x+1})^2=(\sqrt{4x-7})^2$
Simplify.
$\Rightarrow 3x+1=4x-7$
Add $7-3x$ to each side.
$\Rightarrow 3x+1+7-3x=4x-7+7-3x$
Simplify.
$\Rightarrow 8=x$
Check $x=8$.
$\Rightarrow \sqrt{3x+1}=\sqrt{4x-7}$
$\Rightarrow \sqrt{3(8)+1}=\sqrt{4(8)-7}$
$\Rightarrow \sqrt{24+1}=\sqrt{32-7}$
$\Rightarrow \sqrt{25}=\sqrt{25}$
True.
Hence, the solution is $x=8$.
