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.