Express the inequality ​a) using a number​ line, ​b) in interval​ notation, and ​c) as a solution set​ (use set builder​ notation).
xgreater than4

Let's work through the inequality \( x > 4 \) step by step:

### a) **Number Line Representation**:
- On a number line, we represent \( x > 4 \) by placing an **open circle** at 4 (to show that 4 is not included), and shading all numbers to the **right** of 4.

### b) **Interval Notation**:
- Interval notation expresses the range of numbers that satisfy the inequality. Since \( x \) is greater than 4 but does not include 4:
  \[
  (4, \infty)
  \]
  Here, \( ( \) means that 4 is not included, and \( \infty \) indicates that there is no upper bound (because \( x \) can go to infinity).

### c) **Solution Set in Set-Builder Notation**:
- Set-builder notation provides a formal way to describe the solution set:
  \[
  \{ x \in \mathbb{R} \mid x > 4 \}
  \]
  This reads as "the set of all \( x \) in the real numbers such that \( x \) is greater than 4."

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Do you have any questions or want more details on any part of this?

Here are 5 related questions to expand your understanding:
1. How would you represent \( x \geq 4 \) on a number line?
2. What would be the interval notation for \( x \geq 4 \)?
3. How would you represent \( x < 4 \) in set-builder notation?
4. What does it mean when you use brackets vs parentheses in interval notation?
5. How would you express \( 4 \leq x < 10 \) in all three forms?

**Tip**: When using interval notation, always remember that \( ( \) or \( ) \) means the endpoint is not included, and \( [ \) or \( ] \) means the endpoint is included.

Express the inequality ​a) using a number​ line, ​b) in interval​ notation, and ​c) as a solution set​ (use set builder​ notation). x greater than 4

Learn how to express the inequality x > 4 using a number line, interval notation, and set-builder notation. This detailed solution covers key concepts in algebra, including visual representation on the number line and formal expressions in both interval and set-builder notation. Suitable for students in Grades 6-8.

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