Which option correctly describes the values that make the inequality 2m<14

Question

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)

Answer 1

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

\[ m < 7 \]

Now, we can express this solution using set notation. The correct representation would be:

Option #1: {m : m < 7}

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

The other options do not correctly represent the solution:

• Option #2: {7 : 7 < m} does not make sense because it suggests the value 7 is in the set while also requiring that \( m \) is greater than 7.
• Option #3: {m < 7 : m} is not a valid representation in set notation.
• Option #4: {m < 7} also is not a proper representation.

So, the correct answer is:

Option #1: {m : m < 7}