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)
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.