Question

Which option correctly describes the values that make the inequality 2m<14
true when written in set notation?

Option #1: {m:m<7}


Option #2: {7:7<m}


Option #3: {m<7:m}


Option #4: {m<7}


(1 point)
Option #

Answer 1

To solve the inequality \( 2m < 14 \), we can first divide both sides by 2:

\[
m < 7
\]

The solution indicates that any value of \( m \) that is less than 7 will satisfy the inequality.

Now, let’s examine the options given in set notation:

- **Option #1**: \( \{m: m < 7\} \) — This correctly describes the set of all \( m \) such that \( m \) is less than 7.

- **Option #2**: \( \{7: 7 < m\} \) — This describes the set where \( m \) is greater than 7, which is not correct.

- **Option #3**: \( \{m < 7: m\} \) — This does not correctly express the condition and doesn't follow proper set notation conventions.

- **Option #4**: \( \{m < 7\} \) — This does not correctly represent a set of values for \( m \).

The correct option that describes the values that make the inequality \( 2m < 14 \) true when written in set notation is:

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