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Which property of real numbers is shown below?
[tex]\[ -6 + 6 = 0 \][/tex]
A. Associative property of addition B. Commutative property of addition C. Identity property of addition D. Inverse property of addition
We need to identify which property of real numbers this equation demonstrates. The options are:
1. Associative property of addition 2. Commutative property of addition 3. Identity property of addition 4. Inverse property of addition
Let's briefly describe each property:
1. Associative property of addition: This property states that the way in which numbers are grouped when added does not change their sum. For example: [tex]\((a + b) + c = a + (b + c)\)[/tex]
2. Commutative property of addition: This property states that the order in which two numbers are added does not change their sum. For example: [tex]\(a + b = b + a\)[/tex]
3. Identity property of addition: This property states that any number plus zero is the number itself. For example: [tex]\(a + 0 = a\)[/tex]
4. Inverse property of addition: This property states that every number has an additive inverse (a number that when added to the original number results in zero). For example: [tex]\(a + (-a) = 0\)[/tex]
Given the equation: [tex]\[
-6 + 6 = 0
\][/tex]
We see that [tex]\(-6\)[/tex] is the additive inverse of [tex]\(6\)[/tex]. When these two numbers are added, the result is [tex]\(0\)[/tex]. This clearly illustrates the inverse property of addition.
Thus, the property demonstrated by the equation [tex]\(-6 + 6 = 0\)[/tex] is the inverse property of addition.
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