The Inverse Property of Addition states that for every real number [tex]\( a \)[/tex], there exists a unique real number, denoted as [tex]\(-a\)[/tex], such that when [tex]\( a \)[/tex] is added to [tex]\(-a\)[/tex], the result is zero.
To understand this with examples:
1. Consider the real number [tex]\( 5 \)[/tex]. According to the inverse property, we need to find a number which, when added to [tex]\( 5 \)[/tex], results in [tex]\( 0 \)[/tex]. The number that satisfies this property is [tex]\( -5 \)[/tex], because:
[tex]\[
5 + (-5) = 0
\][/tex]
2. Consider the real number [tex]\( -1.33 \)[/tex]. According to the inverse property, to find a number which, when added to [tex]\( -1.33 \)[/tex], results in [tex]\( 0 \)[/tex], we use [tex]\( 1.33 \)[/tex], because:
[tex]\[
-1.33 + 1.33 = 0
\][/tex]
The missing number, [tex]\(-a\)[/tex], is the additive inverse of [tex]\( a \)[/tex]. Therefore, the inverse property of addition can be stated as:
[tex]\[
a + (-a) = 0
\][/tex]
So, the statement that best describes the inverse property of addition is:
[tex]\[
a + (-a) = 0
\][/tex]
