Question

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

Explanation:

Step1: Understand 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 (hollow dot) 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 an inequality \( x > a \), the interval notation is \( (a, \infty) \). Here, \( a = -3 \), so the interval notation should be \( (-3, \infty) \). The original attempt had the interval reversed and the wrong bracket; we use a parenthesis at -3 because -3 is not included, and a parenthesis at \( \infty \) (since \( \infty \) is not a real number and is never included in interval notation).

Answer:

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