https://file.aiquickdraw.com/mathbot/file/1726361246924m64xngy7.jpg

The equation displayed in the image is:

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

Let's solve this step by step.

### Step 1: Isolate the square root term.
To do this, subtract 3 from both sides of the equation:

\[
\sqrt{2x} = 9 - 3
\]
\[
\sqrt{2x} = 6
\]

### Step 2: Square both sides.
Next, square both sides of the equation to eliminate the square root:

\[
(\sqrt{2x})^2 = 6^2
\]
\[
2x = 36
\]

### Step 3: Solve for \(x\).
Now, 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 about the steps? Here are some related questions you might find interesting:

1. How do you handle equations with multiple square root terms?
2. What happens if the equation involves a negative square root?
3. Can you explain why squaring both sides is valid in algebraic manipulation?
4. What would change if the equation had a cube root instead?
5. How can you verify the solution after solving the equation?

**Tip**: Always check your final solution by substituting it back into the original equation to ensure it works correctly!

Learn how to solve the square root equation sqrt(2x) + 3 = 9 with this step-by-step guide. We explore key algebraic concepts, including isolating the square root and squaring both sides. Suitable for students in Grades 7-9.

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