Question

express the interval in set-builder notation and graph the interval on a number line.
$(-\infty, 8)$
select the correct choice below and, if necessary, fill out the answer box to complete your choice
\\(\bigcirc\\) a. the solution set in set-builder notation is \\(\\{x \mid \square\\}\\)
( type an inequality or a compound inequality )
\\(\bigcirc\\) b. the solution set is all real numbers.
\\(\bigcirc\\) c. there is no solution

Explanation:

Step1: Interpret interval notation

The interval $(-\infty, 8)$ means all real numbers less than 8.

Step2: Write set-builder notation

Translate the interval to set-builder form: $\{x \mid x < 8\}$

Step3: Evaluate answer choices

Option A matches the derived set-builder notation; B and C are incorrect as the set is not all real numbers and has solutions.

Answer:

A. The solution set in set-builder notation is $\{x \mid x < 8\}$

Number Line Graph Description:

Draw a horizontal number line. Place an open circle at 8 (to indicate 8 is not included). Shade all the part of the number line to the left of the open circle, extending towards negative infinity.