To understand the inverse property of addition, let's carefully examine the given examples:
1. [tex]\(5 + (-5) = 0\)[/tex]
2. [tex]\(-1.33 + 1.33 = 0\)[/tex]
In both examples, we add a number to its additive inverse (opposite), which results in 0. The additive inverse of a number [tex]\(a\)[/tex] is another number which when added to [tex]\(a\)[/tex] results in [tex]\(0\)[/tex]. The additive inverse of [tex]\(a\)[/tex] is denoted by [tex]\(-a\)[/tex].
Let's rewrite the given equation for a general real number [tex]\(a\)[/tex]:
[tex]\[ a + \square = 0 \][/tex]
From the examples above, we observe that adding [tex]\(-a\)[/tex] to [tex]\(a\)[/tex] results in 0:
[tex]\[ 5 + (-5) = 0 \][/tex]
[tex]\[ -1.33 + 1.33 = 0 \][/tex]
For both cases, the number we added is the additive inverse of the original number. Thus, for any real number [tex]\(a\)[/tex], the additive inverse is [tex]\(-a\)[/tex].
So, the statement that best describes the inverse property of addition is:
[tex]\[ a + (-a) = 0 \][/tex]
This means that the blank should be filled with [tex]\(-a\)[/tex]:
[tex]\[ a + (-a) = 0 \][/tex]
This is the inverse property of addition which states that for any real number [tex]\(a\)[/tex], there exists another real number [tex]\(-a\)[/tex] such that [tex]\(a + (-a) = 0\)[/tex].
