Question

solve. $sqrt4{7x+4}-2=0$
select the correct choice below and fill in any answer boxes present in your choice.
a. the solution(s) is(are) $x = $
(type an integer or a simplified fraction. use a comma to separate answers as needed)
b. there is no solution.

Explanation:

Step1: Isolate the radical term

$\sqrt[4]{7x+4} = 2$

Step2: Raise both sides to 4th power

$(\sqrt[4]{7x+4})^4 = 2^4$
$7x+4 = 16$

Step3: Solve for x

$7x = 16 - 4$
$7x = 12$
$x = \frac{12}{7}$

Step4: Verify the solution

Substitute $x=\frac{12}{7}$ into original equation:
$\sqrt[4]{7\times\frac{12}{7}+4}-2 = \sqrt[4]{12+4}-2 = \sqrt[4]{16}-2 = 2-2=0$, which is valid.

Answer:

A. The solution(s) is(are) $x=\frac{12}{7}$