Question

solve.
\\(\sqrt{3x - 5} = 4\\)

select the correct choice below and fill in any answer boxes present in your choice.
\\(\bigcirc\\) a. \\(x = \square\\)
(simplify your answer. use a comma to separate answers as needed.)
\\(\bigcirc\\) b. there is no solution.

Explanation:

Step1: Square both sides to eliminate root

$$(\sqrt{3x-5})^2 = 4^2$$
$$3x - 5 = 16$$

Step2: Isolate the term with $x$

$$3x = 16 + 5$$
$$3x = 21$$

Step3: Solve for $x$

$$x = \frac{21}{3}$$
$$x = 7$$

Step4: Verify the solution

Substitute $x=7$ into original equation:
$$\sqrt{3(7)-5} = \sqrt{21-5} = \sqrt{16} = 4$$
The solution is valid.

Answer:

A. $x=7$