The question in the image asks about rewriting the set of real numbers greater than 5 in two ways:

1. Set-builder notation
2. Interval notation

Solutions:

1. Set-builder notation:
   In set-builder notation, the set of all real numbers $x$ greater than 5 can be written as:
   $\{x \mid x > 5\}$
   This reads as "the set of all $x$ such that $x > 5$."

2. Interval notation:
   The set of real numbers greater than 5 is represented as:
   $(5, \infty)$
   Here:

   • $(5, \infty)$ means that the set starts from just above 5 (excluding 5) and extends to infinity. Parentheses are used because the boundary (5) is not included.

Do you need further clarification or details?

Related Questions:

1. What is the difference between set-builder and interval notations?
2. How do you represent a set of numbers less than or equal to a specific number in set-builder and interval notations?
3. How do you write the set of all real numbers in interval notation?
4. What is the significance of square brackets ([ \ ]) vs. parentheses (\(( )) in interval notation?
5. Can set-builder notation be used to describe finite sets?

Tip:

Use square brackets ($[$ or \]) for intervals when endpoints are included, and parentheses (\(( or ()) when endpoints are excluded.