Which property yields this -12+36=x-36+36. Additive inverse, additive identity, addition property or commuting property
The property that yields this equation is the addition property.
The given expression is -12 + 36 = x - 36 + 36.
To determine which property is being used, let's analyze each option:
1. Additive inverse: This property states that for any number "a," its additive inverse is "-a," and when the sum of a number and its additive inverse is calculated, the result is zero. However, this property does not apply to the given expression.
2. Additive identity: This property states that for any number "a," the sum of "a" and zero is "a," or "a + 0 = a." Again, this property does not apply to the given expression.
3. Addition property: This property states that if "a = b," then "a + c = b + c." In the given expression, we can observe that the same value (36) is added to both sides of the equation. Thus, the correct choice is the addition property.
4. Commuting property: This property states that the order of numbers within a sum or product does not affect the result. However, the given expression does not involve changing the order of numbers.
Therefore, the correct answer is the addition property.
To determine which property yields the expression -12 + 36 = x - 36 + 36, let's review the properties you mentioned:
1. Additive Inverse: The additive inverse property states that for any real number a, there exists a unique real number -a such that a + (-a) = 0. In this case, we don't see any numbers being negated or involving the additive inverse.
2. Additive Identity: The additive identity property states that for any real number a, a + 0 = a. In the given expression, we have -12 + 36, but we don't see a 0 involved.
3. Addition Property: The addition property refers to the use of addition to combine terms on both sides of an equation. It allows us to add the same quantity to both sides of an equation without changing the equality. This property seems relevant to the given expression, as both sides have the same sum of -12 + 36.
4. Commuting Property: The commuting property of addition states that changing the order of the numbers being added does not affect the sum. In the given expression, we don't see any numbers changing order.
Based on the analysis, the property that yields the expression -12 + 36 = x - 36 + 36 is the addition property, which allows us to add the same quantity to both sides of an equation without changing the equality.