Certainly! To solve the equation
[tex]\[
\sqrt{3x - 2} + 1 = 5,
\][/tex]
we'll go through a series of steps to isolate [tex]\( x \)[/tex]:
### Step 1: Isolate the Square Root Term
Subtract 1 from both sides of the equation to isolate the square root term:
[tex]\[
\sqrt{3x - 2} = 5 - 1.
\][/tex]
Simplifying the right side, we get:
[tex]\[
\sqrt{3x - 2} = 4.
\][/tex]
### Step 2: Remove the Square Root
To eliminate the square root, square both sides of the equation:
[tex]\[
(\sqrt{3x - 2})^2 = 4^2.
\][/tex]
Simplifying both sides, we get:
[tex]\[
3x - 2 = 16.
\][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Now, solve for [tex]\( x \)[/tex] by isolating it on one side of the equation. Start by adding 2 to both sides:
[tex]\[
3x - 2 + 2 = 16 + 2,
\][/tex]
which simplifies to:
[tex]\[
3x = 18.
\][/tex]
Next, divide both sides by 3:
[tex]\[
x = \frac{18}{3},
\][/tex]
which simplifies to:
[tex]\[
x = 6.
\][/tex]
### Conclusion
The solution to the equation [tex]\(\sqrt{3x - 2} + 1 = 5\)[/tex] is [tex]\( x = 6 \)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{x = 6}
\][/tex]
