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To solve the equation \( 6 \sqrt{x - 4} + 1 = 10 \) for \( x \), let's go through it step by step.

### Step 1: Isolate the square root term
Subtract \( 1 \) from both sides:
\[
6 \sqrt{x - 4} = 9
\]

### Step 2: Divide by 6
\[
\sqrt{x - 4} = \frac{9}{6} = 1.5
\]

### Step 3: Square both sides to eliminate the square root
\[
x - 4 = (1.5)^2
\]
\[
x - 4 = 2.25
\]

### Step 4: Solve for \( x \)
Add \( 4 \) to both sides:
\[
x = 2.25 + 4
\]
\[
x = 6.25
\]

### Solution
The solution is:
\[
x = 6.25
\]

Would you like more details on this process or have any questions?

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Here are 5 related questions to expand your understanding:

1. How do you solve an equation with a different square root, such as \( 5 \sqrt{x - 3} + 2 = 12 \)?
2. What happens if the square root term equals a negative number in similar equations?
3. How can you check if a solution is valid in radical equations?
4. Why is it necessary to square both sides of the equation in these problems?
5. How would the solution change if there were a coefficient in front of \( x \) inside the square root?

**Tip:** Always verify your solution by plugging it back into the original equation, especially when dealing with square roots.

Learn how to solve the radical equation 6√(x - 4) + 1 = 10 with a step-by-step solution. This problem covers key algebraic concepts, such as isolating variables, handling square roots, and solving for x. Suitable for students in Grades 8-10.

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