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The given inequality is:

\[
-9k \leq 9
\]

Let's solve this step by step.

1. **Isolate \( k \)**: First, divide both sides of the inequality by \(-9\), but remember that dividing by a negative number reverses the inequality symbol.

\[
k \geq \frac{9}{-9}
\]

2. **Simplify**: 

\[
k \geq -1
\]

This means that \( k \) must be greater than or equal to \(-1\).

### Now, let's check the possible values for \( k \) from the options provided:
- \(-11\): No, because \(-11 < -1\).
- \(-6\): No, because \(-6 < -1\).
- \(-4\): No, because \(-4 < -1\).
- \(-2\): No, because \(-2 < -1\).
- \(-1\): Yes, because \(-1 = -1\).
- \(0\): Yes, because \(0 > -1\).
- \(2\): Yes, because \(2 > -1\).
- \(4\): Yes, because \(4 > -1\).
- \(9\): Yes, because \(9 > -1\).

### Answer choices:
The correct values of \( k \) are \(-1, 0, 2, 4, 9\), and these should be selected.

### Equivalent Inequality:
The equivalent inequality in terms of \( k \) is:
\[
k \geq -1
\]

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Do you have any questions or need further details?

Here are 5 related questions to expand your understanding:
1. What happens to the inequality sign when dividing both sides by a negative number?
2. How would the solution change if the inequality were \( -9k < 9 \) instead?
3. Can you solve the inequality \( 5k + 7 \geq 2k - 1 \)?
4. How do you graph the solution to \( k \geq -1 \) on a number line?
5. What are the rules for solving inequalities involving absolute values?

**Tip**: Always remember to flip the inequality sign when multiplying or dividing both sides by a negative number.

Select the values that make the inequality -9k ≤ 9 true. Then write an equivalent inequality, in terms of k.

This problem involves solving the inequality -9k ≤ 9. Learn how to isolate k, apply the rule for reversing inequalities when dividing by a negative, and identify valid values of k from a given set of numbers. Suitable for Grades 6-8 students.

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