Question

What, if any, is a real solution toA. −51B. 7C. 143 5D. There is no real solution.5x + 1 + 9 = 3?

Answer 1

Given the equation

`\sqrt[]{5x+1\text{ }}\text{ +9 =3}`

Collect like terms

`\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}`

Take the squares of both sides of the equation

`\begin{gathered} (\sqrt[]{5x+1\text{ }})^2=(-6)^2 \\ 5x+1\text{ = 36} \\ \end{gathered}`

Collect like terms

`\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,} \\ (5x)/(5)=(35)/(5) \\ \Rightarrow x=7 \end{gathered}`

Hence, the real solution is 7.

The correct option is B.