Let's solve each of the equations step-by-step to determine which of them could be represented by the given model:
1. Equation: [tex]$-8 - (-10)$[/tex]
To solve this, we need to understand that subtracting a negative number is the same as adding its positive counterpart.
[tex]\[
-8 - (-10) = -8 + 10 = 2
\][/tex]
Thus, [tex]$-8 - (-10) = 2$[/tex].
2. Equation: [tex]$10 - 8$[/tex]
This is a straightforward subtraction problem.
[tex]\[
10 - 8 = 2
\][/tex]
Thus, [tex]$10 - 8 = 2$[/tex].
3. Equation: [tex]$2 - 8$[/tex]
Here, we are subtracting a larger number from a smaller one, resulting in a negative number.
[tex]\[
2 - 8 = -6
\][/tex]
Thus, [tex]$2 - 8 = -6$[/tex].
4. Equation: [tex]$-8 - 6$[/tex]
When subtracting from a negative number, we move further to the left on the number line.
[tex]\[
-8 - 6 = -8 - 6 = -14
\][/tex]
Thus, [tex]$-8 - 6 = -14$[/tex].
5. Equation: [tex]$-8 + 10$[/tex]
Adding a positive number to a negative number can be thought of as reducing the negativity.
[tex]\[
-8 + 10 = 2
\][/tex]
Thus, [tex]$-8 + 10 = 2$[/tex].
Now, we list the results of all equations:
- [tex]$-8 - (-10) = 2$[/tex]
- [tex]$10 - 8 = 2$[/tex]
- [tex]$2 - 8 = -6$[/tex]
- [tex]$-8 - 6 = -14$[/tex]
- [tex]$-8 + 10 = 2$[/tex]
Based on these results, the following equations result in the value 2:
- [tex]$-8 - (-10) = 2$[/tex]
- [tex]$10 - 8 = 2$[/tex]
- [tex]$-8 + 10 = 2$[/tex]
Thus, the equations represented by the number line model are:
- [tex]$-8 - (-10) = 2$[/tex]
- [tex]$10 - 8 = 2$[/tex]
- [tex]$-8 + 10 = 2$[/tex]
