Which statement is true for the expression 6a + 15b − 4a − 8c?
Answer
A. It can be written as 6a + 15b − 8c − 4a by using addition property of equality.
B. It can be written as 6a − 4a + 15b − 8c by using distributive property of addition.
C.It can be written as 6a + 15b − 8c − 4a by using distributive property of addition.
D.It can be written as 6a − 4a + 15b − 8c by using commutative property of addition.
The correct answer is A. It can be written as 6a + 15b − 8c − 4a by using the addition property of equality.
To determine which statement is true for the expression 6a + 15b - 4a - 8c, let's analyze the properties mentioned in each option and see which one can be applied correctly.
A. Addition Property of Equality: This property states that you can rearrange the order of terms when adding them. In this option, it suggests that you can write the expression as 6a + 15b - 8c - 4a. However, this is not correct because the terms 6a and -4a cannot be combined since they have different coefficients.
B. Distributive Property of Addition: This property states that you can distribute addition across terms. In this option, it suggests that you can write the expression as 6a - 4a + 15b - 8c. The expression before and after applying the property remains the same, and the terms with similar variables (-4a and 6a) have been combined correctly. Therefore, this option is correct.
C. Similar to option A, this option incorrectly states that you can write the expression as 6a + 15b - 8c - 4a.
D. Commutative Property of Addition: This property states that you can change the order of terms when adding or multiplying. In this option, it suggests that you can write the expression as 6a - 4a + 15b - 8c. The ordering of the terms is already the same as the original expression, so applying this property does not lead to any change. Therefore, this option is also correct.
To summarize, the correct statement is B: It can be written as 6a - 4a + 15b - 8c by using the distributive property of addition.