Question

express the interval in set-builder notation and graph the interval on a number line.
$(-\infty,4)$
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\\}\\).
\\(\quad\\) (type an inequality or a compound inequality.)
\\(\bigcirc\\) b. the solution set is all real numbers.
\\(\bigcirc\\) c. there is no solution.

Explanation:

Step1: Understand interval notation

The interval \((-\infty, 4)\) means all real numbers \(x\) such that \(x\) is less than \(4\).

Step2: Write set - builder notation

In set - builder notation, we describe the set as \(\{x|x < 4\}\)

Answer:

A. The solution set in set - builder notation is \(\{x\mid x < 4\}\)

For graphing the interval on a number line:

1. Draw a number line.
2. Locate the point \(4\) on the number line.
3. Since the interval is \((-\infty,4)\) (open interval at \(4\)), we draw an open circle at \(4\).
4. Then we shade the region to the left of \(4\) to represent all the numbers less than \(4\).