To solve the equation [tex]\(-2 + \sqrt{3x - 2} = 6\)[/tex], follow these steps:
1. Isolate the square root term:
[tex]\[
-2 + \sqrt{3x - 2} = 6
\][/tex]
Add [tex]\(2\)[/tex] to both sides of the equation:
[tex]\[
\sqrt{3x - 2} = 6 + 2
\][/tex]
Simplify:
[tex]\[
\sqrt{3x - 2} = 8
\][/tex]
2. Remove the square root by squaring both sides of the equation:
[tex]\[
(\sqrt{3x - 2})^2 = 8^2
\][/tex]
Simplify:
[tex]\[
3x - 2 = 64
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Add [tex]\(2\)[/tex] to both sides of the equation:
[tex]\[
3x - 2 + 2 = 64 + 2
\][/tex]
Simplify:
[tex]\[
3x = 66
\][/tex]
Divide both sides by [tex]\(3\)[/tex]:
[tex]\[
x = \frac{66}{3}
\][/tex]
Simplify:
[tex]\[
x = 22
\][/tex]
Therefore, the solution to the equation [tex]\(-2 + \sqrt{3x - 2} = 6\)[/tex] is [tex]\(x = 22\)[/tex].
Hence, the correct answer is [tex]\( \boxed{22} \)[/tex].
