Answer
2
Work Step by Step
The third line is incorrect because the square of a binomial, $(a+b)^2$ is not $a^2+b^2$ but should be $a^2+2ab+b^2$.
The correct solution is as follows:
\begin{array}{l}\require{cancel}
\sqrt{5x-1}+4=7
\\\\
\sqrt{5x-1}=7-4
\\\\
\sqrt{5x-1}=3
\\\\
\left( \sqrt{5x-1} \right)^2=(3)^2
\\\\
5x-1=9
\\\\
5x=9+1
\\\\
5x=10
\\\\
x=\dfrac{10}{5}
\\\\
x=2
.\end{array}
