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To solve the equation:

\[
\sqrt{2x} + 3 = 9
\]

we can follow these steps:

### Step 1: Isolate the square root term
Subtract 3 from both sides of the equation:

\[
\sqrt{2x} = 9 - 3
\]

\[
\sqrt{2x} = 6
\]

### Step 2: Square both sides
To eliminate the square root, square both sides of the equation:

\[
(\sqrt{2x})^2 = 6^2
\]

\[
2x = 36
\]

### Step 3: Solve for \( x \)
Divide both sides by 2:

\[
x = \frac{36}{2}
\]

\[
x = 18
\]

### Solution
The solution to the equation is:

\[
x = 18
\]

Would you like further details or have any questions?

Here are some related questions to consider:

1. How would the solution change if the equation were \(\sqrt{2x} + 3 = 10\) instead?
2. What if the square root applied to \((2x + 3)\) instead, like \(\sqrt{2x + 3} = 9\)?
3. How can you verify the solution by substituting \(x = 18\) back into the original equation?
4. What are the restrictions on \(x\) when dealing with square root equations?
5. How would the equation change if there was a coefficient in front of the square root, like \(2\sqrt{2x} + 3 = 9\)?

**Tip:** Always check for extraneous solutions when dealing with square roots by substituting back into the original equation.

Learn how to solve the square root equation \(\sqrt{2x} + 3 = 9\) with a detailed step-by-step solution. This problem involves isolating terms, squaring both sides, and solving for x, covering key algebraic concepts. Suitable for students in Grades 8-10.

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