https://r2.erweima.ai/mathbot/image/1726594392431vdqtm7yz.jpg

The equation shown in the image is:

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

### Step-by-step solution:

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

2. **Eliminate the square root**:
   Square both sides of the equation to remove the square root:
   \[
   (\sqrt{2x})^2 = 6^2
   \]
   \[
   2x = 36
   \]

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

Thus, the solution is \( x = 18 \).

Would you like more details or have any questions? 

Here are five related questions to consider:
1. What happens if the equation had a negative constant added instead of positive?
2. How do you solve similar equations when there’s a cube root instead of a square root?
3. Can you generalize a method for solving equations involving roots and constants?
4. What if the expression inside the square root had been more complex, e.g., \( \sqrt{3x + 5} \)?
5. How can you verify solutions to equations involving roots?

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

Learn how to solve the equation √(2x) + 3 = 9 with a detailed step-by-step solution. This problem covers key algebraic concepts, including isolating the square root term, squaring both sides, and solving linear equations. Suitable for students in Grades 8-10.

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