Which property of algebra should first be applied to 6a−14b+3a−6+21b−18a in order to determine whether it is equivalent to −9a+7b−6 ? (1 point)
Responses
Commutative Property
Commutative Property
Associative Property
Associative Property
Identity Property
Identity Property
Distributive Property
not an answer
Apologies for that. The property that should first be applied to determine whether the two expressions are equivalent is the Distributive Property.
To determine whether the expression 6a−14b+3a−6+21b−18a is equivalent to −9a+7b−6, we need to simplify both expressions and compare them. The property of algebra that should first be applied is the Distributive Property.
The Distributive Property states that for any real numbers a, b, and c, a(b + c) = ab + ac. This property allows us to distribute a value across a sum or difference.
In this case, we need to apply the Distributive Property to simplify the given expression and determine if it is equivalent to the other expression:
Starting with 6a−14b+3a−6+21b−18a, we can group like terms together:
(6a + 3a - 18a) + (-14b + 21b) - 6
Now, we can combine the like terms within each group:
(-9a) + (7b) - 6
This simplifies to: -9a + 7b - 6
Comparing this simplified expression to the expression -9a + 7b - 6, we can see that they are equal. Thus, the original expression 6a−14b+3a−6+21b−18a is indeed equivalent to −9a+7b−6.
Therefore, to determine whether the expressions are equivalent, the first property of algebra that should be applied is the Distributive Property.