Question

For each statement, identify the property that justifies it:

A) The Addition Property of Equality
B) The Substitution Property of Equality
C) The Multiplication Property of Equality
D) The Reflexive Property
E) The Transitive Property

1. If 4m + n = 7 and n = 3, then 4n + 3 = 7.
2. If a = -5, then 2a = -10.
3. If 3x = y, then y = 3x.
4. If 4w - 1 = 11, then 4w = 12.
5. If a + b = c, and c = d^2, then a + b = d^2.
6. 6y = 6y.
7. If -8q = -56, then q = 7.
8. If 5k = -25, then 5k - 1 = -25 - 1.
9. -3(2x - 5) = -6x + 15.
Choose the correct property for each statement.

Answer 1

The properties of equality such as Substitution, Multiplication, Reflexive, Addition, and Transitive properties justify the given mathematical statements, allowing us to maintain equality while manipulating algebraic equations.

Step-by-step explanation:

To determine which property justifies each statement, we will match them as follows:

1. If 4m + n = 7 and n = 3, then 4n + 3 = 7 is justified by the Substitution Property of Equality (B).
2. If a = -5, then 2a = -10 is justified by the Multiplication Property of Equality (C).
3. If 3x = y, then y = 3x is justified by the Reflexive Property (D).
4. If 4w - 1 = 11, then 4w = 12 is justified by the Addition Property of Equality (A).
5. If a + b = c, and c = d^2, then a + b = d^2 is justified by the Transitive Property (E).
6. 6y = 6y is justified by the Reflexive Property (D).
7. If -8q = -56, then q = 7 is justified by the Multiplication Property of Equality because we are effectively dividing both sides by -8 (C).
8. If 5k = -25, then 5k - 1 = -25 - 1 is not based on an equality property but on an action performed on both sides of an equation. Therefore, none of the given properties A to E directly applies.
9. -3(2x - 5) = -6x + 15 is an example of the Distributive Property (C).

Remember that these properties are fundamental to solving algebraic equations and allow us to manipulate them, maintaining the equality to find the values of unknown variables.