Question

solve.
\\(\sqrt{5x - 6} = 8\\)

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

$$(\sqrt{5x-6})^2 = 8^2$$
$$5x - 6 = 64$$

Step2: Isolate the term with x

$$5x = 64 + 6$$
$$5x = 70$$

Step3: Solve for x

$$x = \frac{70}{5}$$
$$x = 14$$

Step4: Verify the solution

Substitute $x=14$ into original equation:
$$\sqrt{5(14)-6} = \sqrt{70-6} = \sqrt{64} = 8$$
This matches the right-hand side, so the solution is valid.

Answer:

A. $x=14$