Which property yields -12+36=x-36+36. Additive inverse, additive identity, addiction property commutive property
The property that yields -12+36=x-36+36 is the additive inverse property.
The property that yields -12+36=x-36+36 is the additive inverse property.
The additive inverse property states that for any real number a, there exists a number -a such that a + (-a) = 0.
In this case, -12 is the additive inverse of 12, since 12 + (-12) = 0. Therefore, we can rewrite the equation as:
-12 + 36 = (x - 36) + 36
Now, we can simplify the equation:
24 = x
So, the solution to the equation is x = 24.
Therefore, the property used was the additive inverse property.
To identify which property is being used in the equation -12 + 36 = x - 36 + 36, let's go through the properties one by one:
1. Additive Inverse Property: According to this property, the sum of a number and its additive inverse equals zero. In the given equation, we don't have any downward dash ("-") right before the numbers or variables. Therefore, the additive inverse property is not being used here.
2. Additive Identity Property: According to this property, the sum of any number and zero is equal to the original number. In the given equation, we have the number 36 being added to both sides. Since 36 + 0 is equal to 36, we can conclude that the Additive Identity Property is being used here.
3. Addition Property: This property states that you can add the same number to both sides of an equation without changing the equality. In the given equation, we are adding 36 to both sides. Therefore, we can say that the Addition Property is being used here.
4. Commutative Property: This property states that you can change the order of addition or multiplication without changing the result. In the given equation, we don't have any rearrangements or changes in the order of addition. Therefore, the Commutative Property is not being used here.
In conclusion, based on the analysis above, the property being used in the equation -12 + 36 = x - 36 + 36 is the Additive Identity Property and the Addition Property.