Question

graph the set {x | x > -3} on the number line. then, write the set using interval notation.

Explanation:

Step1: Analyze the inequality

The set is defined as \( \{x \mid x > -3\} \), which means all real numbers greater than -3.

Step2: Graph on the number line

• Locate -3 on the number line.
• Since \( x > -3 \) (not \( x \geq -3 \)), we use an open circle at -3 to indicate that -3 is not included in the set.
• Then, draw an arrow to the right of -3 to show all numbers greater than -3.

Step3: Write in interval notation

For the interval notation, we use a parenthesis when the endpoint is not included. Since \( x > -3 \), the interval starts at -3 (not included) and goes to positive infinity. So the interval notation is \( (-3, \infty) \).

Answer:

• Graph: Open circle at -3, arrow to the right.
• Interval Notation: \((-3, \infty)\)