Sure! We can solve the problem [tex]\(-4 + 2 + (-2)\)[/tex] using the commutative property of addition. The commutative property tells us that the order in which we add numbers does not change the sum. Let's break this down step-by-step in three different ways:
### Method 1
1. Initial Expression: [tex]\(-4 + 2 + (-2)\)[/tex]
2. Step-by-Step Calculation:
- First, add [tex]\(-4\)[/tex] and [tex]\(2\)[/tex]:
[tex]\[
-4 + 2 = -2
\][/tex]
- Then add [tex]\(-2\)[/tex]:
[tex]\[
-2 + (-2) = -4
\][/tex]
3. The result for this method is [tex]\(-4\)[/tex].
### Method 2
1. Rearranged Order: [tex]\(2 + (-2) + (-4)\)[/tex]
2. Step-by-Step Calculation:
- First, add [tex]\(2\)[/tex] and [tex]\(-2\)[/tex]:
[tex]\[
2 + (-2) = 0
\][/tex]
- Then add [tex]\(-4\)[/tex]:
[tex]\[
0 + (-4) = -4
\][/tex]
3. The result for this method is also [tex]\(-4\)[/tex].
### Method 3
1. Another Rearranged Order: [tex]\((-2) + (-4) + 2\)[/tex]
2. Step-by-Step Calculation:
- First, add [tex]\(-2\)[/tex] and [tex]\(-4\)[/tex]:
[tex]\[
-2 + (-4) = -6
\][/tex]
- Then add [tex]\(2\)[/tex]:
[tex]\[
-6 + 2 = -4
\][/tex]
3. The result for this method is [tex]\(-4\)[/tex] as well.
In summary, using the commutative property of addition and altering the order of terms, we consistently find that the sum is:
[tex]\[
-4
\][/tex]
