3.- Notice that:
[tex]\sqrt[]{12}=\sqrt[]{4\cdot3}=2\sqrt[]{3}\text{.}[/tex]
Therefore, we can rewrite the given equation as follows:
[tex]2\sqrt[]{3}x-3\sqrt[]{3}x+5=4.[/tex]
Adding like terms we get:
[tex]-\sqrt[]{3}x+5=4.[/tex]
Subtracting 5 from the above equation we get:
[tex]\begin{gathered} -\sqrt[]{3}x+5-5=4-5, \\ -\sqrt[]{3}x=-1. \end{gathered}[/tex]
Dividing the above equation by -√3 we get:
[tex]\begin{gathered} \frac{-\sqrt[]{3}x}{-\sqrt[]{3}}=\frac{-1}{-\sqrt[]{3}}, \\ x=\frac{1}{\sqrt[]{3}}\text{.} \end{gathered}[/tex]
Finally, recall that:
[tex]\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{3}\text{.}[/tex]
Therefore:
[tex]x=\frac{\sqrt[]{3}}{3}\text{.}[/tex]
Answer: Option C.
