Question

Name the property used to make the following:

If -20 = -13 - 7b, then -7 = -7b
a. Addition Property of Equality (APOE)
b. Substitution Property
c. Distributive Property
d. Subtraction Property of Equality (SPOE)
e. Division Property of Equality (DPOE)

Answer 1

The property used to go from -20 = -13 - 7b to -7b = -7 is the Division Property of Equality (DPOE), which states that equal quantities remain equal if divided by the same nonzero number.

Step-by-step explanation:

The question asks to name the property used to make a specific algebraic manipulation. The given expression is If -20 = -13 - 7b, then -7b = -7. This manipulation is the result of division on both sides of the equation by the same number, which does not change the equality. The correct property for this action is the Division Property of Equality (DPOE). This property states that if two equal quantities are divided by the same nonzero number, the quotients are also equal.