Question

Which option correctly describes the values that make the inequality
$2m\lt 14$ true when written in set notation?
Option \#1: $\{ m:m\lt 7\} $
Option \#2: $\{ 7:7\lt m\} $
Option \#3: $\{ m\lt 7:m\} $
Option \#4: $\{ m\lt 7\} $
(1 point)
Option \# $\square $ correctly states the values that make the inequality true in set
notation.

Answer 1

First, let's solve the inequality \(2m < 14\).

1. Divide both sides of the inequality by 2:
\[
m < 7
\]

Now, we want to determine which option correctly expresses the solution \(m < 7\) in set notation.

- **Option \#1**: \(\{ m:m < 7 \}\) - This expresses the set of all \(m\) such that \(m < 7\), which correctly describes the solution.

- **Option \#2**: \(\{ 7:7 < m \}\) - This describes the set of 7, which doesn't correctly reflect the solution since it implies values greater than 7.

- **Option \#3**: \(\{ m < 7:m \}\) - This is not a correct format for set notation. It mixes the components incorrectly.

- **Option \#4**: \(\{ m < 7 \}\) - This does not appropriately define a set with elements; it simply lists the inequality.

Based on the above analysis, the correct option that captures the solution to the inequality \(2m < 14\) in set notation is:

**Option \#1: \(\{ m:m < 7 \}\)**.

Thus, the answer is Option \#1.