Question

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

Answer 1

so is m:m<7 correct or 7:7<m

Answer 2

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

1. Divide both sides of the inequality by 2:
\[
m < \frac{14}{2}
\]
\[
m < 7
\]

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

In set notation, this can be expressed as:
\[
\{ m \in \mathbb{R} \mid m < 7 \}
\]
or simply,
\[
(-\infty, 7)
\]
This interval notation indicates that \( m \) can take any value from negative infinity up to, but not including, 7.

Thus, the correct description of the values that make the inequality \( 2m < 14 \) true in set notation is:
\[
(-\infty, 7)
\]

Answer 3

The correct way to express the values of \( m \) that satisfy the inequality \( 2m < 14 \) (which simplifies to \( m < 7 \)) in set notation is:

\[
\{ m \mid m < 7 \}
\]

This means "the set of all \( m \) such that \( m \) is less than 7."

So, \( m : m < 7 \) is correct.

On the other hand, \( 7 : 7 < m \) would be incorrect for our case, as this would imply the set of values greater than 7, which does not reflect the original inequality.

In summary, the correct expression is:
\[
\{ m \mid m < 7 \}
\]