Answer:
B.[tex]x=\frac{4}{15}[/tex]
Step-by-step explanation:
- [tex]\frac{\sqrt{4-3x}}{\sqrt{3x} } =2[/tex]can be simplify by doing some algebra.
- Particulary, in this case, [tex]\frac{\sqrt{4-3x}}{\sqrt{3x} } =\sqrt{\frac{4-3x}{3x} }[/tex], because of the distributive property with respect to division and multiplication.
- Then, by dividing numerator and denominator by 3x inside the power we get [tex]\sqrt{\frac{\frac{4}{3x}-1}{1}}=\sqrt{\frac{4}{3x}-1} =2[/tex].
- To dispose of the squared root, we raise to power 2 both sides of the equation, to obtain the following expression: [tex]\frac{4}{3x}-1=4[/tex].
- Finally, we just have to clear out the value of x from this expression, by addding 1 both sides of the equation: [tex]\frac{4}{3x}=5[/tex], and then by multiplying both sides by 3x, and then dividing the result by 15. This yields [tex]x=\frac{4}{15}[/tex]
