Let's solve the equation step by step.

Given equation: $\frac{x}{-6} - 7 = -11$

Step 1: Add 7 to both sides

$\frac{x}{-6} - 7 + 7 = -11 + 7$ This simplifies to: $\frac{x}{-6} = -4$

Step 2: Multiply both sides by -6 to isolate $x$

$(-6) \times \frac{x}{-6} = (-4) \times (-6)$ This simplifies to: $x = 24$

Step 3: Check the solution

Substitute $x = 24$ back into the original equation: $\frac{24}{-6} - 7 = -11$ $-4 - 7 = -11$ This is true, so $x = 24$ is the correct solution.

Final Answer:

$x = 24$

Would you like further details or have any questions?

Here are 5 related questions:

1. How would the solution change if the equation was $\frac{x}{6} - 7 = -11$?
2. What happens when you add or subtract negative numbers?
3. Can you explain how multiplying by a negative number affects the result?
4. What does isolating the variable mean in solving equations?
5. How can you check if your solution is correct in any equation?

Tip: Always perform the same operation on both sides of an equation to maintain equality.