Question

part c - slightly

1. \\(\sqrt{2x} = 6\\)

Explanation:

State the given equation

We are given the radical equation:

$$\sqrt{2x} = 6$$

Square both sides

To eliminate the radical, square both sides:

$$(\sqrt{2x})^2 = 6^2$$

$$2x = 36$$

Solve for x

Divide both sides by 2:

$$x = \frac{36}{2}$$

$$x = 18$$

Verify the solution

Substitute \(x = 18\) back into the original equation:

$$\sqrt{2(18)} = \sqrt{36} = 6$$

The solution is valid.

Answer:

\(x = 18\)