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Write An inequality to describe each of the following graphs;then write An equivalente negated inequality 

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 \( 4 \).

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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.

Write an inequality to describe each of the following graphs; then write an equivalent negated inequality.

Learn how to describe inequalities using a number line with the range -3 ≤ x < 4, and how to write the equivalent negated inequality x < -3 or x ≥ 4. This problem covers key algebraic concepts and is suitable for students in Grades 7-9.

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