Proofs Flashcard

Front

What is the Subtraction Property of Equality?

Back

If a = b, then a - c = b - c for any number c.

Front

What is the Addition Property of Equality?

Back

If a = b, then a + c = b + c for any number c.

Front

What is the Multiplication Property of Equality?

Back

If a = b, then a * c = b * c for any number c.

Front

What is the Division Property of Equality?

Back

If a = b and c ≠ 0, then a / c = b / c.

Front

What is the Transitive Property of Equality?

Back

If a = b and b = c, then a = c.

Front

What does 'Given' mean in proofs?

Back

It refers to the information that is provided as a starting point for the proof.

Front

What is the purpose of a proof in mathematics?

Back

To provide a logical argument that demonstrates the truth of a statement.

Front

How do you justify the step '7x = 21' in the equation 3x + 2 = 23 - 4x?

Back

By using the Addition Property of Equality to isolate the variable.

Front

What is the first step in solving the equation 3x + 2 = 23 - 4x?

Back

Combine like terms to get 7x + 2 = 23.

Front

What is the final solution for x in the equation 3x + 2 = 23 - 4x?

Back

x = 3.