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Let's break down and solve the given inequalities step by step.

The problem contains two inequalities:

### 1st Inequality: 
\[
n - 3 - 8n \geq 11
\]

### 2nd Inequality:
\[
-n + 6 > -13n + 18
\]

#### **Solving the 1st inequality:**
\[
n - 3 - 8n \geq 11
\]

Combine like terms:
\[
-7n - 3 \geq 11
\]

Add 3 to both sides:
\[
-7n \geq 14
\]

Divide both sides by -7 (and reverse the inequality sign because of division by a negative number):
\[
n \leq -2
\]

#### **Solving the 2nd inequality:**
\[
-n + 6 > -13n + 18
\]

Add \(13n\) to both sides:
\[
12n + 6 > 18
\]

Subtract 6 from both sides:
\[
12n > 12
\]

Divide both sides by 12:
\[
n > 1
\]

### Final solution:
- From the first inequality, \(n \leq -2\)
- From the second inequality, \(n > 1\)

So the solution is \(n \leq -2\) or \(n > 1\).

### Graphing the solution:
- For \(n \leq -2\), this will be a closed circle at -2 with a ray extending to the left.
- For \(n > 1\), this will be an open circle at 1 with a ray extending to the right.

Would you like a more detailed breakdown or have any other questions?

Here are five related questions:
1. How do we determine when to reverse inequality signs?
2. What is the graphical representation of "or" inequalities?
3. What would happen if the second inequality had a "greater than or equal to" instead?
4. Can you explain the difference between closed and open circles on the graph?
5. How would the solution change if the inequalities were connected by "and" instead of "or"?

**Tip:** Always check whether you need to reverse the inequality sign when multiplying or dividing by negative numbers.

Solve for n and graph the solution. n - 3 - 8n ≥ 11 or -n + 6 > -13n + 18

Learn how to solve the inequality n - 3 - 8n ≥ 11 or -n + 6 > -13n + 18 with a step-by-step solution. This problem covers key algebraic concepts, including combining like terms and inequality properties. Suitable for students in Grades 8-10.

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