We are given two inequalities to solve:

1. \(-x - 9 < -12\)
2. \(-20 \geq -x - 9\)

Let's solve them one by one.

### Inequality 1: 
\(-x - 9 < -12\)

1. Add 9 to both sides:
   \[
   -x < -12 + 9
   \]
   \[
   -x < -3
   \]

2. Multiply both sides by \(-1\) and reverse the inequality:
   \[
   x > 3
   \]

So, for the first inequality, \(x > 3\).

---

### Inequality 2:
\(-20 \geq -x - 9\)

1. Add 9 to both sides:
   \[
   -20 + 9 \geq -x
   \]
   \[
   -11 \geq -x
   \]

2. Multiply both sides by \(-1\) and reverse the inequality:
   \[
   11 \leq x
   \]
   \[
   x \geq 11
   \]

So, for the second inequality, \(x \geq 11\).

---

### Combined solution:
From both inequalities, we need to satisfy:
- \(x > 3\)
- \(x \geq 11\)

The solution that satisfies both conditions is \(x \geq 11\).

---

### Final Answer:
The solution to the system of inequalities is:
\[
x \geq 11
\]

Would you like further details or explanations?

---

Here are 5 related questions:
1. How do you solve systems of linear inequalities?
2. What happens when you multiply or divide an inequality by a negative number?
3. Can inequalities have no solution? If so, how?
4. How can you graph inequalities on a number line?
5. What are compound inequalities, and how are they solved?

**Tip:** Always remember to reverse the inequality when multiplying or dividing by a negative number!

Learn how to solve the system of linear inequalities −x−9<−12 and −20≥−x−9 with a step-by-step explanation. This solution includes reversing inequalities when multiplying by a negative number and combining solutions. Suitable for students in Grades 8-10.

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