It seems like you're trying to define a function \( G(x) = 2x + 6 \) and possibly asking to substitute \( x = x + 3 \) into it.

Let me walk you through this:

### Given:
\[ G(x) = 2x + 6 \]

Now, if you want to substitute \( x = x + 3 \) into the function, let's do that step by step.

### Substitute \( x = x + 3 \) into \( G(x) \):
\[ G(x + 3) = 2(x + 3) + 6 \]

Expand the terms:
\[ G(x + 3) = 2x + 6 + 6 \]

Simplify:
\[ G(x + 3) = 2x + 12 \]

So, after the substitution, the new expression for \( G(x + 3) \) is:
\[ G(x + 3) = 2x + 12 \]

Would you like to dive deeper into this concept or have any questions?

### Related questions:
1. How do you find the domain and range of the function \( G(x) \)?
2. What is the graphical interpretation of shifting a function by \( x + 3 \)?
3. How does the slope of the function \( G(x) = 2x + 6 \) affect its behavior?
4. Can we solve for \( x \) if \( G(x) = 0 \)? How?
5. How would \( G(x) \) change if we had a different coefficient of \( x \)?

### Tip:
Substituting values or expressions into a function helps you see how the function behaves with different inputs.

Explore how to substitute variables in the function G(x) = 2x + 6 by replacing x with x + 3. This problem covers algebraic concepts of function substitution and linear transformations, ideal for students in Grades 8-10.

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