Answer :
To determine which choice is equivalent to the expression [tex]\sqrt{9x} - \sqrt{4x} + 4\sqrt{x}[/tex], let's simplify each of the square roots this expression contains.
Simplify [tex]\sqrt{9x}[/tex]:
- [tex]\sqrt{9x} = \sqrt{9} \times \sqrt{x} = 3\sqrt{x}[/tex].
Simplify [tex]\sqrt{4x}[/tex]:
- [tex]\sqrt{4x} = \sqrt{4} \times \sqrt{x} = 2\sqrt{x}[/tex].
Now, substitute these simplified results back into the original expression:
[tex]3\sqrt{x} - 2\sqrt{x} + 4\sqrt{x}[/tex]
Combine like terms:
- [tex](3\sqrt{x} - 2\sqrt{x}) + 4\sqrt{x} = 1\sqrt{x} + 4\sqrt{x} = 5\sqrt{x}[/tex].
Therefore, the expression [tex]\sqrt{9x} - \sqrt{4x} + 4\sqrt{x}[/tex] simplifies to [tex]5\sqrt{x}[/tex].
Upon reviewing the provided choices, it appears there is an error as none of the given options match this simplified result.
If option A is suggested as [tex]3\sqrt{2x} + 4[/tex], cross-checking against the correct simplified form shows they are not equivalent. This suggests the option provided does not represent a correct simplification.