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 #___ correctly states the values that make the inequality true in set notation.

Answer 1

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

\[
m < 7
\]

Now we want to express this in set notation. The correct way to write the solution set is:

\[
\{ m : m < 7 \}
\]

This means "the set of all \( m \) such that \( m \) is less than 7."

Now, reviewing the options provided:

- **Option #1:** \{m : m < 7\} **(Correct)**
- **Option #2:** \{7 : 7 < m\} **(Incorrect)**
- **Option #3:** \{m < 7 : m\} **(Incorrect)**
- **Option #4:** \{m < 7\} **(Incorrect)**

The only option that correctly states the values that make the inequality true in set notation is:

**Option #1**: {m : m < 7}

So, the answer is **Option #1**.