To address the question of what property justifies the statement that if 3x > 4 and 3x > 10, then 3x must also be greater than 6, we need to explore the properties of inequalities.
The key concept here is the Transitive Property of Inequality. This property states that if a > b and b > c, then it follows that a > c. In your question, we consider the inequalities:
- 3x > 4
- 3x > 10
From these two inequalities, it is clear that:
- Since 3x is greater than 10, it is certainly greater than any number less than or equal to 10, including 6.
- Therefore, we can conclude that if 3x > 10, then it must also be true that 3x > 6.
In summary, the Transitive Property allows us to establish the inequality: if 3x > 10, then 3x > 6 must also hold true, thereby justifying the original statement.