Answer :
To simplify the expression [tex]\sqrt{9x} - \sqrt{4x} + 4\sqrt{x}[/tex], we can break it down into simpler parts by computing each square root individually and simplifying.
The term [tex]\sqrt{9x}[/tex] can be simplified because 9 is a perfect square. [tex]\sqrt{9x} = \sqrt{9} \cdot \sqrt{x} = 3\sqrt{x}[/tex].
The term [tex]\sqrt{4x}[/tex] can also be simplified because 4 is a perfect square. [tex]\sqrt{4x} = \sqrt{4} \cdot \sqrt{x} = 2\sqrt{x}[/tex].
The expression now becomes:
[tex]3\sqrt{x} - 2\sqrt{x} + 4\sqrt{x}[/tex]
We can combine the like terms:
[tex](3 - 2 + 4)\sqrt{x} = 5\sqrt{x}[/tex]
Now, let's compare this result with the given multiple-choice options:
- Option A is [tex]3\sqrt{2x} + 4\sqrt{x}[/tex], which does not match our simplified expression.
- Option B is 17, which is not equivalent to our expression.
Since neither of the provided options matches, it seems there might be an error in the options given or in the transcription of the expression.
To conclude, the expression [tex]\sqrt{9x} - \sqrt{4x} + 4\sqrt{x}[/tex] simplifies to [tex]5\sqrt{x}[/tex], but this does not match any of the given options.