To solve the inequality \( 2m < 14 \), we can first divide both sides by 2:
\[ m < 7 \]
The solution indicates that any value of \( m \) that is less than 7 will satisfy the inequality.
Now, let’s examine the options given in set notation:
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Option #1: \( {m: m < 7} \) — This correctly describes the set of all \( m \) such that \( m \) is less than 7.
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Option #2: \( {7: 7 < m} \) — This describes the set where \( m \) is greater than 7, which is not correct.
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Option #3: \( {m < 7: m} \) — This does not correctly express the condition and doesn't follow proper set notation conventions.
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Option #4: \( {m < 7} \) — This does not correctly represent a set of values for \( m \).
The correct option that describes the values that make the inequality \( 2m < 14 \) true when written in set notation is:
Option #1: \( {m: m < 7} \).
1 answer