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Let's solve the inequality:

\[
8 + 10n \geq -2
\]

### Step-by-Step Solution:
1. Subtract 8 from both sides to isolate the term with the variable:
\[
10n \geq -2 - 8
\]
\[
10n \geq -10
\]

2. Divide both sides by 10:
\[
n \geq \frac{-10}{10}
\]
\[
n \geq -1
\]

### Solution:
The inequality is \( n \geq -1 \).

### Graphing the Solution:
On a number line, we represent \( n \geq -1 \). This means the solution includes all numbers greater than or equal to \(-1\). Since it is "greater than or equal to," the point at \(-1\) is closed (filled) to show that \(-1\) is included in the solution.

- Draw a closed circle at \(-1\).
- Draw a ray extending to the right, indicating that all values greater than \(-1\) are solutions.

Would you like further details or clarifications? 

### Related Questions:
1. How do you solve inequalities with variables on both sides?
2. What happens if you multiply or divide an inequality by a negative number?
3. How would the solution change if the inequality was \( n > -1 \) instead of \( n \geq -1 \)?
4. Can you explain how to check if a number is a solution to an inequality?
5. What are the differences between strict and non-strict inequalities?

**Tip:** Always be careful with inequalities—if you multiply or divide by a negative number, you must flip the inequality sign!

Solve the inequality 8 + 10n ≥ -2 and graph the solution.

Learn how to solve and graph the inequality 8 + 10n ≥ -2. This problem includes isolating the variable, solving the inequality, and graphing the solution on a number line. Suitable for students in Grades 6-8.

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