Certainly! To verify the equation [tex]\(a + (b + c) = (a + b) + c\)[/tex] for the given values [tex]\(a = -8\)[/tex], [tex]\(b = 4\)[/tex], and [tex]\(c = -1\)[/tex], let's go through the calculations step-by-step:
1. Compute [tex]\(b + c\)[/tex]:
[tex]\[
b + c = 4 + (-1)
\][/tex]
[tex]\[
b + c = 3
\][/tex]
2. Compute [tex]\(a + (b + c)\)[/tex]:
[tex]\[
a + (b + c) = -8 + 3
\][/tex]
[tex]\[
a + (b + c) = -5
\][/tex]
3. Compute [tex]\(a + b\)[/tex]:
[tex]\[
a + b = -8 + 4
\][/tex]
[tex]\[
a + b = -4
\][/tex]
4. Compute [tex]\((a + b) + c\)[/tex]:
[tex]\[
(a + b) + c = -4 + (-1)
\][/tex]
[tex]\[
(a + b) + c = -5
\][/tex]
Now, we need to compare the results from steps 2 and 4 to verify if they are equal:
- The left-hand side [tex]\(a + (b + c) = -5\)[/tex]
- The right-hand side [tex]\((a + b) + c = -5\)[/tex]
Since both sides of the equation have the same value, [tex]\(-5\)[/tex], we have verified that:
[tex]\[
a + (b + c) = (a + b) + c
\][/tex]
Thus, the equation holds true for the given values [tex]\(a = -8\)[/tex], [tex]\(b = 4\)[/tex], and [tex]\(c = -1\)[/tex].
