The number line graph you provided shows a range between two points:

• The range starts at $-3$ (closed dot) and goes to $4$ (open dot).
• The arrow heads indicate the inequality involves numbers between $-3$ and $4$.

1. The Inequality:

Since the graph shows that $-3$ is included (closed dot) and $4$ is not included (open dot), the inequality describing this is: $-3 \leq x < 4$ This inequality describes the set of numbers between $-3$ (inclusive) and $4$ (exclusive).

2. The Negated Inequality:

The negation of the inequality involves values outside the range from $-3$ to $4$. Negating $-3 \leq x < 4$ gives: $x < -3 \quad \text{or} \quad x \geq 4$ This is because the negation means the values are either less than $-3$ or greater than or equal to $4$.

Would you like any further explanation on inequalities or negations? Here are five related questions you might explore:

1. How do you represent an inequality on a number line when both endpoints are inclusive?
2. How do you negate a compound inequality involving "or" statements?
3. Can you solve real-life problems using inequalities?
4. What are the differences between strict and non-strict inequalities?
5. How does interval notation correspond to inequality notation?

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