Sure, let's go through each problem in detail using a number line to visualize the sums and differences.
### 7. [tex]\(-4 + (-5)\)[/tex]
To find [tex]\(-4 + (-5)\)[/tex] using a number line:
1. Start at [tex]\(-4\)[/tex] on the number line.
2. Since we are adding [tex]\(-5\)[/tex], move 5 units to the left (since adding a negative number means moving to the left).
3. After moving 5 units left from [tex]\(-4\)[/tex], you will land at [tex]\(-9\)[/tex].
So, [tex]\(-4 + (-5) = -9\)[/tex].
### 9. [tex]\(6 - (-4)\)[/tex]
To find [tex]\(6 - (-4)\)[/tex] using a number line:
1. Start at 6 on the number line.
2. Subtracting a negative number is the same as adding its positive counterpart. So, [tex]\(6 - (-4)\)[/tex] is equivalent to [tex]\(6 + 4\)[/tex].
3. Move 4 units to the right from 6.
4. After moving 4 units right from 6, you will land at 10.
So, [tex]\(6 - (-4) = 10\)[/tex].
### 8. [tex]\(-2 + 10\)[/tex]
To find [tex]\(-2 + 10\)[/tex] using a number line:
1. Start at [tex]\(-2\)[/tex] on the number line.
2. Add 10 units by moving 10 units to the right.
3. After moving 10 units right from [tex]\(-2\)[/tex], you will land at 8.
So, [tex]\(-2 + 10 = 8\)[/tex].
### 10. [tex]\(5(-17) + (-11)\)[/tex]
To solve [tex]\(5 \cdot (-17) + (-11)\)[/tex] step-by-step:
1. First, calculate [tex]\(5 \cdot (-17)\)[/tex]:
- Multiply 5 by -17 which results in -85.
2. Then add [tex]\(-11\)[/tex] to [tex]\(-85\)[/tex]:
- Start at [tex]\(-85\)[/tex] on the number line.
- Move 11 units to the left.
- After moving 11 units left from [tex]\(-85\)[/tex], you will land at [tex]\(-96\)[/tex].
So, [tex]\(5(-17) + (-11) = -96\)[/tex].
The results for each part are:
- 7. [tex]\(-4 + (-5) = -9\)[/tex]
- 9. [tex]\(6 - (-4) = 10\)[/tex]
- 8. [tex]\(-2 + 10 = 8\)[/tex]
- 10. [tex]\(5(-17) + (-11) = -96\)[/tex]
