To fully simplify the expression \( 2x - 2y + 6 - 5x - 7y \), follow these steps:

1. **Combine like terms for \( x \)**:
   \[
   2x - 5x = -3x
   \]

2. **Combine like terms for \( y \)**:
   \[
   -2y - 7y = -9y
   \]

3. **Combine the constant terms**:
   \[
   6 \text{ (no other constants to combine)}
   \]

Now, combine all the simplified terms together:

\[
-3x - 9y + 6
\]

So, the fully simplified expression is:
\[
-3x - 9y + 6
\]

Would you like more details on any step, or do you have any questions?

Here are some related questions:

1. How do you identify like terms in algebraic expressions?
2. What are some strategies for simplifying more complex algebraic expressions?
3. Can you provide an example of simplifying an expression with more variables?
4. How does factoring differ from simplifying?
5. What is the importance of the order of operations in simplifying expressions?
6. How do you simplify expressions with fractions?
7. How can we simplify expressions with exponents?
8. What is the next step if we wanted to factor the simplified expression?

**Tip:** Always group and simplify like terms first to make algebraic expressions easier to handle.

Learn how to fully simplify the expression 2x - 2y + 6 - 5x - 7y with a detailed step-by-step guide. This problem involves combining like terms and simplifying algebraic expressions. Suitable for Grades 7-9.

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