To solve the equation \(\sqrt{2x} + 3 = 9\), follow these steps:

1. **Isolate the square root term:**
   \[
   \sqrt{2x} + 3 = 9
   \]
   Subtract 3 from both sides:
   \[
   \sqrt{2x} = 6
   \]

2. **Square both sides to eliminate the square root:**
   \[
   (\sqrt{2x})^2 = 6^2
   \]
   Simplifying this, we get:
   \[
   2x = 36
   \]

3. **Solve for \(x\):**
   Divide both sides by 2:
   \[
   x = \frac{36}{2}
   \]
   Simplifying this, we get:
   \[
   x = 18
   \]

So, the solution to the equation \(\sqrt{2x} + 3 = 9\) is \(x = 18\).

Would you like more details or have any questions?

Here are 8 related questions:

1. What are the steps to isolate a square root in an equation?
2. How do you square both sides of an equation?
3. What happens if squaring both sides introduces extraneous solutions?
4. How do you check if a solution to a square root equation is valid?
5. Can you solve \(\sqrt{3x} + 5 = 11\) in a similar way?
6. How would you solve the equation \(\sqrt{4x - 1} = 5\)?
7. What are common mistakes to avoid when solving square root equations?
8. How do you solve an equation with a cube root, like \(\sqrt[3]{x} + 2 = 4\)?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they are valid.

Learn how to solve the equation √(2x) + 3 = 9 with a detailed step-by-step solution. This problem involves isolating a square root term and applying basic algebraic operations. Suitable for high school students in Grades 9-12.

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