Simplify 4x + 8x using the properties of operations.
A 4x + 8
B 12x²
C 4 + 8x
D 12x
The Correct Answer and Explanation is :
The correct answer is D: 12x.
Explanation:
To simplify the expression ( 4x + 8x ), we can apply the properties of operations, particularly the commutative property of addition and distributive property.
- Commutative Property of Addition: This property states that the order of addition does not change the sum. So, we can rewrite the expression as:
[
4x + 8x = 8x + 4x
]
(Although this step is not strictly necessary, it’s helpful to understand that the terms can be reordered.) - Combining Like Terms: Both ( 4x ) and ( 8x ) are “like terms,” meaning they both contain the variable ( x ). To combine them, we add the coefficients (the numbers in front of ( x )) together. The coefficients are 4 and 8. So:
[
4x + 8x = (4 + 8)x
]
[
4x + 8x = 12x
]
This shows that the expression simplifies to ( 12x ). - Distributive Property: Another way to approach this is by factoring out the common factor of ( x ) from both terms:
[
4x + 8x = (4 + 8)x
]
This simplifies to:
[
12x
]
The distributive property states that you can factor out a common factor from terms that have it, and then multiply it by the sum of the remaining terms.
Why the Other Options Are Incorrect:
- A: ( 4x + 8 ): This is not correct because it represents adding ( 4x ) to a constant, but the original expression doesn’t have a constant term like 8; both terms are multiples of ( x ).
- B: ( 12x^2 ): This is incorrect because the terms ( 4x ) and ( 8x ) do not involve squaring the variable. We are simply adding the ( x )-terms, not multiplying them.
- C: ( 4 + 8x ): This is not correct because it changes the order of the terms, and the variable ( x ) is not combined in the proper way.
Thus, the correct simplified form of ( 4x + 8x ) is 12x.