We are given the inequality:

\[
1 - 3x \geq 9
\]

and the set of values for \( x \) is \( \{ -4, -5, -6 \} \).

### Step 1: Solve the inequality.

To isolate \( x \), follow these steps:

1. Subtract 1 from both sides of the inequality:
   \[
   1 - 3x - 1 \geq 9 - 1
   \]
   \[
   -3x \geq 8
   \]

2. Divide both sides by -3. Remember that when you divide or multiply an inequality by a negative number, the inequality sign flips:
   \[
   x \leq \frac{8}{-3}
   \]
   \[
   x \leq -\frac{8}{3}
   \]

### Step 2: Check the values of \( x \) in the set \( \{-4, -5, -6\} \).

We want the values of \( x \) that satisfy \( x \leq -\frac{8}{3} \) (which is approximately \( -2.67 \)):

- For \( x = -4 \), \( -4 \leq -\frac{8}{3} \) is true.
- For \( x = -5 \), \( -5 \leq -\frac{8}{3} \) is true.
- For \( x = -6 \), \( -6 \leq -\frac{8}{3} \) is true.

### Conclusion:
All the values in the set \( \{-4, -5, -6\} \) satisfy the inequality \( 1 - 3x \geq 9 \).

Would you like more details on any specific step?

Here are some related questions to expand on this:

1. What happens when we multiply or divide inequalities by negative numbers?
2. How do we graph inequalities on a number line?
3. What are the implications of solving inequalities with absolute values?
4. Can we solve inequalities involving quadratic equations?
5. How do we handle systems of inequalities?

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

Discover how to solve the inequality 1 - 3x ≥ 9 using the values x ∈ {-4, -5, -6}. This detailed explanation covers key algebra concepts, including how to solve inequalities, flipping the inequality sign, and verifying solutions for given values. Suitable for students in Grades 6-8.

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