The question is asking you to identify the property of inequality used in the given scenario:

Given: For all expressions $a$, $b$, and $c$,

• If $a + b = c$ and $b > 0$, then $c > a$.

The correct answer is the Addition property of inequality.

Explanation:

This is based on the principle that if you add a positive number to any number, the result is greater than the original number. In this case:

• Since $b > 0$, adding $b$ to $a$ means $c = a + b$.
• This makes $c$ greater than $a$ because you're adding a positive amount to $a$.

Therefore, the property used here is called the Addition property.

Would you like more details or have any questions about this?

Follow-up questions to expand your understanding:

1. What is the Transitive property of inequalities?
2. How does the Comparison property differ from the Addition property?
3. Can you give an example where the Subtraction property of inequality is used?
4. In what scenarios would the Addition property not hold true?
5. How can the Addition property of inequalities be used to solve linear equations?

Tip:

When dealing with inequalities, always remember that adding or subtracting the same positive number to both sides preserves the inequality.