Explanation
We are given the following equation:
[tex]\sqrt{5x-2}-1=3[/tex]
We are required to determine the value of x.
This is achieved thus:
[tex]\begin{gathered} \sqrt{5x-2}-1=3 \\ \text{ Add 1 to both sides} \\ \sqrt{5x-2}-1+1=3+1 \\ \sqrt{5x-2}=4 \\ \text{ Square both sides } \\ (\sqrt{5x-2})^2=4^2 \\ 5x-2=16 \\ \text{ Collect like terms } \\ 5x=16+2 \\ 5x=18 \\ \text{ Divide both sides by 5} \\ \frac{5x}{5}=\frac{18}{5} \\ x=\frac{18}{5} \end{gathered}[/tex]
Hence, the answer is:
[tex]x=\frac{18}{5}[/tex]
