Problem 8 - College Algebra Essentials

Question

Express each interval in set-builder notation and graph the interval on a number line. $$(3, \infty)$$

Step-by-Step Solution

Answer

The interval \((3, \infty)\) in set-builder notation is represented as \{x | x \in R, x > 3\}. On the number line, the interval is represented with an open circle at 3 and an arrow pointing right, indicating that the interval includes all real numbers greater than 3.

Step 1: Set Builder Notation

The interval \((3, \infty)\) in set-builder notation will be represented as: \{x | x \in R, x > 3\}, meaning the set of all x such that x is a real number and x is greater than 3.

Step 2: Drawing The Number Line

Start by drawing a straight horizontal line, which represents the number line. Now mark a point on the line for the number 3.

Step 3: Representing The Interval On Number line

On the number line, an open circle is drawn at 3 because 3 is not included in the interval. Afterwards, an arrow pointing to the right is drawn from 3 to indicate that the interval continues indefinitely in positive direction.