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The following examples illustrate the inverse property of addition. Study the examples, then choose the statement that best describes the property.

[tex]\[
\begin{array}{l}
5 + (-5) = 0 \\
-1.33 + 1.33 = 0
\end{array}
\][/tex]

Inverse property of addition: For real numbers,

[tex]\[ a + \square = 0 \][/tex]

Sagot :

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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]
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