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The equation given is:

\[
6 + x = x + 6
\]

To solve this, let's first subtract \( x \) from both sides:

\[
6 + x - x = x + 6 - x
\]

This simplifies to:

\[
6 = 6
\]

Since this is a true statement for all values of \( x \), the solution to the equation is all real numbers. The correct answer to this question is:

\[
\boxed{\text{C. All whole numbers}}
\]

Would you like more details, or do you have any questions about this?

Here are 5 related questions to expand your understanding:
1. What does it mean for an equation to have no solution?
2. How do you recognize when an equation has infinitely many solutions?
3. Can you solve a similar equation with different constants, like \(5 + x = x + 8\)?
4. How would the solution change if the equation was \(6 + x = x + 7\)?
5. What is the difference between solving linear and quadratic equations?

**Tip:** When both variables cancel out, check the remaining constants. If the result is always true, the solution is all real numbers; if false, there is no solution.

Explore how to solve the identity equation 6 + x = x + 6, which simplifies to a true statement for all values of x. This basic algebra problem helps students understand when an equation has infinitely many solutions, making it ideal for middle school students in grades 6-8.

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