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

Question

Option #1: {m:m<7}

Option #2: {7:7<m}

Option #3: {m<7:m}

Option #4: {m<7}

Answer 1

To solve the inequality \(2m < 14\), we start by isolating \(m\):

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

This means that all values of \(m\) that are less than 7 satisfy the inequality.

Now, let's evaluate the options given in set notation:

1. Option #1: {m:m<7} - This means the set of all \(m\) such that \(m < 7\), which is correct.

2. Option #2: {7:7<m} - This means the set containing the number 7 where \(7 < m\), which is incorrect as it does not describe values less than 7.

3. Option #3: {m<7:m} - This is not standard set notation and is incorrectly formatted; it doesn't properly convey the solution.

4. Option #4: {m<7} - This does not properly represent the set of all \(m\) values less than 7; it looks like it's stating \(m\) itself is a condition rather than a set.

The correct answer is Option #1: {m:m<7}.