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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.

1 answer

To solve the inequality \( 2m < 14 \), we first divide both sides by 2:

\[ m < 7 \]

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

In set notation, this can be expressed as:

\[ { m : m < 7 } \]

Now let's analyze the options given:

  • Option #1: {m:m<7} - This correctly describes the values that satisfy the inequality.
  • Option #2: {7:7<m} - This incorrectly describes values greater than 7, which does not satisfy the inequality.
  • Option #3: {m<7:m} - This syntax is incorrect for set notation.
  • Option #4: {m<7} - This also does not properly describe the condition in set notation.

Therefore, the correct option is:

Option #1: {m:m<7}