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The inequality given is:

\[
\frac{x}{-2} < 4
\]

To solve this inequality for \( x \), follow these steps:

1. **Multiply both sides by -2**: Since we're multiplying by a negative number, the inequality sign must reverse.

\[
x > 4 \times (-2)
\]

2. **Simplify**:

\[
x > -8
\]

### Inequality Solution: 
The solution is \( x > -8 \), meaning all values greater than \(-8\).

### Graphing the Solution on a Number Line:
- Draw a number line.
- Place an open circle at \(-8\) because \( x \) is strictly greater than \(-8\) (not equal to \(-8\)).
- Shade the number line to the right of \(-8\), indicating that all values greater than \(-8\) are solutions.

### Final Answer:
- **Inequality Notation**: \( x > -8 \)
- On the number line, place an open circle at \(-8\) and shade everything to the right of it.

Would you like more details or have any other questions?

Here are 5 related questions for further practice:
1. Solve the inequality \( \frac{x}{3} > 5 \) and graph it.
2. How do you handle inequalities when multiplying or dividing by a negative number?
3. Solve and graph the inequality \( \frac{x}{4} \leq -2 \).
4. What is the difference between open and closed circles on a number line?
5. Solve \( 2x - 5 \geq 3 \) and graph the solution.

**Tip**: Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number.

Solve for x and graph the solution on the number line for the inequality x / -2 < 4.

Learn how to solve and graph the inequality x / -2 < 4. This problem demonstrates key concepts in algebra and inequalities. The solution involves reversing the inequality sign when multiplying by a negative number. Suitable for students in Grades 7-9.

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