Let's solve the equation step by step to determine which option is correct. The equation given is:

$-9x - 7 = 27x - 6(6x - 7)$

Step 1: Distribute the $-6$ on the right-hand side:

$-9x - 7 = 27x - 6(6x - 7) = 27x - 36x + 42$

Now, the equation looks like: $-9x - 7 = 27x - 36x + 42$

Step 2: Simplify the terms on the right-hand side:

$-9x - 7 = -9x + 42$

Step 3: Add $9x$ to both sides to eliminate the $-9x$:

$-7 = 42$

This is a contradiction since $-7$ does not equal $42$. Therefore, the equation has no solution.

Conclusion:

The correct answer is A. no real solutions.

Would you like any further clarification or details?

Here are 5 related questions:

1. How do you solve linear equations with distribution and combining like terms?
2. What are some common strategies to check for no-solution cases in equations?
3. How can you identify whether an equation has no solution or infinite solutions?
4. Can you explain how to handle equations with variables on both sides?
5. What happens when you encounter a contradiction while solving an equation?

Tip: Always simplify each side of an equation fully before moving terms across the equal sign to avoid errors!