Let's carefully analyze the equation provided:
[tex]\[
-6 + 6 = 0
\][/tex]
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.
