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To solve the inequality \(-6 < x - 11\), follow these steps:

1. Start with the inequality:
   \[
   -6 < x - 11
   \]

2. Add 11 to both sides to isolate \(x\):
   \[
   -6 + 11 < x
   \]

3. Simplify the left side:
   \[
   5 < x
   \]
   This can also be written as:
   \[
   x > 5
   \]

Thus, the number that belongs in the green box is **5**.

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

Here are 5 related questions to expand your understanding:

1. How would the inequality change if it were \(-6 \leq x - 11\)?
2. What happens if you have a negative variable coefficient, like \(-2x < 4\)?
3. How would you graph the solution \(x > 5\) on a number line?
4. What is the effect of multiplying or dividing both sides of an inequality by a negative number?
5. How can you check if a number is a solution to an inequality?

**Tip:** When solving inequalities, always remember to reverse the inequality sign when you multiply or divide by a negative number.

This lesson covers how to solve the linear inequality -6 < x - 11 using basic algebraic techniques. Learn how to isolate the variable x and solve for values greater than 5. Suitable for Grades 7-8 students.

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