Alright, let's go through this step-by-step using the Addition Property of Equality.
1. The Addition Property of Equality states that for any real numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], if [tex]\(a = b\)[/tex], then [tex]\(a + c = b + c\)[/tex].
2. Let's start by considering the given condition: [tex]\(a = b\)[/tex].
3. According to this property, if [tex]\(a = b\)[/tex] and we add the same real number [tex]\(c\)[/tex] to both sides of the equation, the equality should still hold.
4. So we express this as:
[tex]\[
a + c
\][/tex]
Since [tex]\(a = b\)[/tex], we can replace [tex]\(a\)[/tex] with [tex]\(b\)[/tex] in the expression above:
[tex]\[
b + c
\][/tex]
5. Therefore, if [tex]\(a = b\)[/tex], then:
[tex]\[
a + c = b + c
\][/tex]
Given the result we know, if [tex]\(a\)[/tex] and [tex]\(b\)[/tex] both are 1 and [tex]\(c\)[/tex] is also 1, we substitute these values:
[tex]\[
a + c = 1 + 1 = 2
\][/tex]
Thus, [tex]\(a+c=2\)[/tex] when the conditions [tex]\(a = b = 1\)[/tex] and [tex]\(c = 1\)[/tex] are applied. So, the final answer using the Addition Property of Equality is:
[tex]\[
2
\][/tex]
