Question

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 first divide both sides by 2:

\[ m < 7 \]

In set notation, this can be expressed as:

\[ { m : m < 7 } \]

Now, let's evaluate the options provided:

1. Option #1: \( { m : m < 7 } \) - This is correct.
2. Option #2: \( { 7 : 7 < m } \) - This is incorrect because it describes the set of values greater than 7, which does not represent our solution.
3. Option #3: \( { m < 7 : m } \) - This is incorrectly structured and not a proper set notation.
4. Option #4: \( { m < 7 } \) - This is also not proper set notation as it does not include the variable in the correct way.

Thus, the correct option is:

Option #1: \( { m : m < 7 } \).