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}

(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: \({ m : m < 7 }\).