https://file.aiquickdraw.com/mathbot/file/17267763230605uq8sc11.jpg

The inequality shown in the image is:

\[
-8x - 9 > -21
\]

### Let's solve for \( x \):

1. **Add 9 to both sides** to eliminate the constant term on the left:
   \[
   -8x - 9 + 9 > -21 + 9
   \]
   Simplifying this:
   \[
   -8x > -12
   \]

2. **Divide both sides by -8**. When dividing by a negative number, you must **reverse the inequality sign**:
   \[
   x < \frac{-12}{-8}
   \]
   Simplifying the fraction:
   \[
   x < 1.5
   \]

### Final solution:
\[
x < 1.5
\]

Would you like further details, or do you have any questions?

Here are some related questions to consider:
1. How do you solve inequalities with variables on both sides?
2. What is the importance of reversing the inequality sign when dividing by a negative number?
3. How does solving an inequality differ from solving an equation?
4. Can you explain how to check if a value satisfies the inequality?
5. What are some real-life applications of inequalities?

**Tip**: When working with inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Learn how to solve the linear inequality -8x - 9 > -21 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequality rules and reversal of the inequality sign. Suitable for students in Grades 8-10.

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