Let's verify the associative property of addition for the given values [tex]\( a = -35 \)[/tex], [tex]\( b = 10 \,\text{cm} \)[/tex], and [tex]\( c = -5 \)[/tex].
First, we will evaluate the left side of the equation [tex]\( a + (b + c) \)[/tex]:
1. Calculate the expression inside the parentheses:
[tex]\[
b + c = 10 + (-5) = 10 - 5 = 5
\][/tex]
2. Now, add this result to [tex]\( a \)[/tex]:
[tex]\[
a + (b + c) = -35 + 5 = -30
\][/tex]
So, the left side of the equation [tex]\( a + (b + c) \)[/tex] is equal to [tex]\(-30\)[/tex].
Next, we will evaluate the right side of the equation [tex]\( (a + b) + c \)[/tex]:
1. First, calculate the expression inside the parentheses:
[tex]\[
a + b = -35 + 10 = -25
\][/tex]
2. Now, add this result to [tex]\( c \)[/tex]:
[tex]\[
(a + b) + c = -25 + (-5) = -25 - 5 = -30
\][/tex]
So, the right side of the equation [tex]\( (a + b) + c \)[/tex] is also equal to [tex]\(-30\)[/tex].
Finally, we compare both sides:
[tex]\[
a + (b + c) = -30 \quad \text{and} \quad (a + b) + c = -30
\][/tex]
Since both sides are equal, we have verified that:
[tex]\[
a + (b + c) = (a + b) + c
\][/tex]
Thus, the associative property of addition holds true for the given values [tex]\( a = -35 \)[/tex], [tex]\( b = 10 \,\text{cm} \)[/tex], and [tex]\( c = -5 \)[/tex].
