Sure! Let's solve each part of the problem step-by-step using a number line.
### Part (a): Solve [tex]\(-10 + 2\)[/tex]
1. Start at [tex]\(-10\)[/tex] on the number line. This is your initial point.
2. Adding [tex]\(2\)[/tex] means moving [tex]\(2\)[/tex] units to the right (since adding a positive number is moving to the right).
3. From [tex]\(-10\)[/tex], moving [tex]\(2\)[/tex] units to the right brings you to [tex]\(-8\)[/tex].
So, the answer to [tex]\(-10 + 2\)[/tex] is [tex]\(-8\)[/tex].
### Part (b): Solve [tex]\(7 - (-9)\)[/tex]
1. Start at [tex]\(7\)[/tex] on the number line. This is your initial point.
2. Subtracting [tex]\(-9\)[/tex] is the same as adding [tex]\(9\)[/tex] (since subtracting a negative is the same as adding the positive counterpart). This means moving [tex]\(9\)[/tex] units to the right.
3. From [tex]\(7\)[/tex], moving [tex]\(9\)[/tex] units to the right brings you to [tex]\(16\)[/tex].
So, the answer to [tex]\(7 - (-9)\)[/tex] is [tex]\(16\)[/tex].
Combining these results:
- For part (a), [tex]\(-10 + 2 = -8\)[/tex].
- For part (b), [tex]\(7 - (-9) = 16\)[/tex].
Hence, your final answers are:
[tex]\[ \boxed{-8} \quad \text{and} \quad \boxed{16} \][/tex]
