Let's break down the problem step by step:

We are given the function:

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

And we are also told that \( F(x) = 10 \). To find the value of \( x \), we set the function equal to 10 and solve for \( x \):

\[
\sqrt{2x - 6} = 10
\]

### Step 1: Square both sides to eliminate the square root:
\[
(\sqrt{2x - 6})^2 = 10^2
\]
\[
2x - 6 = 100
\]

### Step 2: Add 6 to both sides:
\[
2x = 106
\]

### Step 3: Divide by 2 to solve for \( x \):
\[
x = \frac{106}{2} = 53
\]

Thus, the value of \( x \) is:

\[
x = 53
\]

Would you like further details or have any questions?

Here are some related questions to expand your understanding:
1. What happens if \( F(x) = -10 \)?
2. Can a square root function ever give negative values?
3. What is the domain of the function \( F(x) = \sqrt{2x - 6} \)?
4. How would you solve \( F(x) = 0 \) for this function?
5. What happens to the value of \( F(x) \) as \( x \) increases?

**Tip**: When solving equations involving square roots, always remember to check if the result satisfies the original equation!

Learn how to solve the square root function F(x) = sqrt(2x - 6) when F(x) equals 10, with a detailed step-by-step solution. This problem involves key algebraic concepts such as solving square root equations and properties of functions. Suitable for students in Grades 9-10.

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