Answer :

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].