Question

1. $6sqrt{x - 2} + 1 = 13$

Explanation:

Step1: Isolate the radical term.

Subtract 1 from both sides:
$6\sqrt{x-2} = 13 - 1$
$6\sqrt{x-2} = 12$

Step2: Solve for the radical.

Divide both sides by 6:
$\sqrt{x-2} = \frac{12}{6}$
$\sqrt{x-2} = 2$

Step3: Eliminate the square root.

Square both sides of the equation:
$(\sqrt{x-2})^2 = 2^2$
$x - 2 = 4$

Step4: Solve for x.

Add 2 to both sides:
$x = 4 + 2$
$x = 6$

Answer:

$x=6$