https://file.aiquickdraw.com/mathbot/file/17260779668060qucir8g.jpg

We are given the inequality:

\[
\frac{x}{-3} < 8
\]

To solve this inequality:

### Step 1: Eliminate the fraction
Multiply both sides of the inequality by \(-3\). Note that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign reverses.

\[
x > 8 \times -3
\]

\[
x > -24
\]

### Step 2: Graph the solution
On the number line, the solution \( x > -24 \) is represented by an open circle at \( -24 \) and an arrow pointing to the right, indicating all values greater than \( -24 \).

### Final Solution:
The solution is \( x > -24 \), which should be graphed accordingly.

Would you like more details on the steps involved, or do you have any questions?

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Here are 5 related questions for further understanding:
1. How would the graph change if the inequality were \( \frac{x}{-3} \leq 8 \)?
2. What happens if we multiply or divide by a negative number when solving inequalities?
3. How can you check if your solution to an inequality is correct?
4. How does solving linear inequalities differ from solving linear equations?
5. Can this inequality solution be represented in interval notation?

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

Solve \( \frac{x}{-3} < 8 \). Graph the solution.

Learn how to solve the inequality \( \frac{x}{-3} < 8 \) and graph the solution on a number line. This problem covers essential algebraic concepts, including inequalities and the rule for multiplying or dividing by negative numbers. The solution is suitable for students in Grades 7-9.

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