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The problem asks whether the statement is true or false, and, if false, to make the necessary changes to produce a true statement.

The statement in question says:
"The first step in solving \( \sqrt{3x - 5} = x + 4 \) is to square both sides, obtaining \( x = 5x^2 + 10 \)."

Let's analyze the solution step-by-step.

### Correct steps:
1. **Equation given**: \( \sqrt{3x - 5} = x + 4 \)
2. **Square both sides**: \( (\sqrt{3x - 5})^2 = (x + 4)^2 \)
    - This leads to: \( 3x - 5 = (x + 4)^2 \)
3. **Expand the right side**: 
   \[
   (x + 4)^2 = x^2 + 8x + 16
   \]
   So, after squaring and expanding, you get:
   \[
   3x - 5 = x^2 + 8x + 16
   \]

Clearly, the given statement that "squaring both sides gives \( x = 5x^2 + 10 \)" is **false**.

### Options analysis:
- **A**: Incorrect. The first step is to square both sides, but this results in \( 3x - 5 = x^2 + 8x + 16 \), not \( x + 5 = \dots \).
- **B**: Correct! The statement is false because squaring both sides results in \( 3x - 5 = x^2 + 8x + 16 \), not \( x = 5x^2 + 10 \).
- **C**: Incorrect for similar reasons to A.
- **D**: Incorrect because the statement is not true.

### Final Answer:
The correct answer is **B**.

Would you like a detailed explanation on how to solve the equation further? 

Here are some related questions you could explore:
1. What are the next steps to solve \( 3x - 5 = x^2 + 8x + 16 \)?
2. How do you factor quadratic equations like \( x^2 + 8x + 16 \)?
3. What are extraneous solutions, and how do they apply to radical equations?
4. How do you verify solutions for equations involving square roots?
5. Can you always square both sides of an equation involving square roots?

**Tip**: Always check for extraneous solutions when solving radical equations, as squaring both sides can introduce invalid solutions.

Determine whether the following statement is true or false. The first step in solving sqrt(3x - 5) = x + 4 is to square both sides, obtaining x = 5x^2 + 10.

Learn how to solve the radical equation sqrt(3x - 5) = x + 4. The problem involves algebraic techniques such as squaring both sides and expanding binomials, leading to a quadratic equation. This detailed solution is ideal for students in Grades 9-10.

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