Given the equation
[tex]\sqrt[]{5x+1\text{ }}\text{ +9 =3}[/tex]
Collect like terms
[tex]\begin{gathered} \sqrt[]{5x+1\text{ }}\text{ +9 =3} \\ \sqrt[]{5x+1\text{ }}\text{ =3}-9 \\ \Rightarrow\sqrt[]{5x+1\text{ }}\text{ =-6} \end{gathered}[/tex]
Take the squares of both sides of the equation
[tex]\begin{gathered} (\sqrt[]{5x+1\text{ }})^2=(-6)^2 \\ 5x+1\text{ = 36} \\ \end{gathered}[/tex]
Collect like terms
[tex]\begin{gathered} 5x+1\text{ =36} \\ \Rightarrow5x\text{ = 36-1} \\ 5x=35 \\ \text{divide both sides by the cofficient of x, which is 5.} \\ \text{thus,} \\ \frac{5x}{5}=\frac{35}{5} \\ \Rightarrow x=7 \end{gathered}[/tex]
Hence, the real solution is 7.
The correct option is B.
