Question

select the correct answer. solve the equation for x. $6 - \sqrt{4 + 3x} = 2$ \bigcirc 6 \bigcirc 4 \bigcirc 2 \bigcirc 1

Explanation:

Step1: Isolate the radical term

$6 - 2 = \sqrt{4+3x}$
$\implies 4 = \sqrt{4+3x}$

Step2: Square both sides

$4^2 = (\sqrt{4+3x})^2$
$\implies 16 = 4 + 3x$

Step3: Solve for x

$16 - 4 = 3x$
$\implies 12 = 3x$
$\implies x = \frac{12}{3} = 4$

Step4: Verify the solution

Substitute $x=4$ into original equation:
$6 - \sqrt{4+3\times4} = 6 - \sqrt{16} = 6-4=2$, which matches the right-hand side.

Answer:

○ 4