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

Given the inequality \( x > 4 \):

### a) **Number line:**
On a number line, this inequality means that \( x \) includes all values greater than 4. We represent this by drawing an open circle at \( 4 \) (since \( 4 \) is not included) and shading the line to the right of \( 4 \).

### b) **Interval notation:**
In interval notation, the solution is written as:
\[
(4, \infty)
\]
Where the round bracket "(" at 4 means 4 is not included, and \( \infty \) means the numbers go on infinitely in the positive direction.

### c) **Set-builder notation:**
In set-builder notation, the inequality is expressed as:
\[
\{x \mid x > 4\}
\]
This means the set of all \( x \) such that \( x \) is greater than 4.

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Do you want more details or have any questions? 

Here are 5 related questions:
1. How would the number line change for \( x \geq 4 \)?
2. What would interval notation be for \( x < 4 \)?
3. How is the solution set written if \( x \leq 4 \)?
4. Can you graph inequalities with two bounds, like \( 2 < x < 6 \)?
5. How would the solution change for \( x > -3 \)?

**Tip**: Always remember, use an open circle for strict inequalities (like \( > \) or \( < \)) and a closed circle for inclusive inequalities (like \( \geq \) or \( \leq \)).

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

Understand how to solve and represent the inequality x > 4 using a number line, interval notation, and set-builder notation. This guide provides a step-by-step approach, perfect for students in Grades 6-8 looking to master inequalities.

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