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 can first divide both sides by 2:

\[
m < 7
\]

The set of values that satisfy this inequality can be expressed in set notation as \(\{ m : m < 7 \}\).

Now, let's evaluate the options:

- **Option #1**: \(\{ m : m < 7 \}\) - This is correct.
- **Option #2**: \(\{ 7 : 7 < m \}\) - This is incorrect; it does not represent the solution to \(2m < 14\).
- **Option #3**: \(\{ m < 7 : m \}\) - This is not standard set notation.
- **Option #4**: \(\{ m < 7 \}\) - This is also not standard set notation.

The correct option is **Option #1**: \(\{ m : m < 7 \}\).