To solve the equation \(\sqrt{2x} - 7 = 3\), we need to isolate \(x\). Here's the step-by-step process:

1. **Add 7 to both sides:**

   \[
   \sqrt{2x} = 3 + 7
   \]

   \[
   \sqrt{2x} = 10
   \]

2. **Square both sides to eliminate the square root:**

   \[
   2x = 10^2
   \]

   \[
   2x = 100
   \]

3. **Divide both sides by 2:**

   \[
   x = \frac{100}{2}
   \]

   \[
   x = 50
   \]

So, the solution is \(x = 50\).

Would you like more details or have any questions?

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Here are 5 related questions to explore:

1. What happens if you subtract 7 from both sides of the equation instead of adding it?
2. How would the solution change if the equation was \(\sqrt{3x} - 7 = 3\) instead?
3. What if the equation had been \(\sqrt{2x} + 7 = 3\) instead?
4. How do you solve equations that involve a cube root instead of a square root?
5. What are some methods to check if your solution is correct?

**Tip:** Always double-check your work by plugging the solution back into the original equation.

Learn how to solve the radical equation √(2x) - 7 = 3 using a step-by-step approach. This example covers algebraic techniques, including adding constants, squaring both sides, and solving for x. Perfect for students in Grades 8-10.

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