Question

graph the set {x | x < 2} on the number line. then, write the set using interval notation.

Explanation:

Step1: Understand the set

The set \(\{x \mid x < 2\}\) includes all real numbers less than 2.

Step2: Determine interval notation

For numbers less than 2, the interval starts from negative infinity (since there's no lower bound) and goes up to, but not including, 2. In interval notation, we use \((-\infty, 2)\) because we don't include 2 (so we use a parenthesis) and negative infinity is always paired with a parenthesis.

Answer:

\((-\infty, 2)\)

(For the graphing part: On the number line, we place an open circle at 2 (because 2 is not included in the set) and draw an arrow to the left to represent all numbers less than 2.)