Certainly! Let's break down the problem step by step.
### Step-by-Step Solution:
1. Identify the given integers:
- The first integer is [tex]\(-6\)[/tex].
- The second integer is [tex]\(-4\)[/tex].
2. Find the sum of [tex]\(-6\)[/tex] and [tex]\(-4\)[/tex]:
[tex]\[
-6 + (-4) = -10
\][/tex]
3. Write the mathematical expression to subtract [tex]\(-15\)[/tex] from the sum of [tex]\(-6\)[/tex] and [tex]\(-4\)[/tex]:
[tex]\[
\text{Sum of } (-6) \text{ and } (-4) - (-15)
\][/tex]
Substituting the sum we found:
[tex]\[
-10 - (-15)
\][/tex]
4. Simplify the expression:
Subtracting a negative number is the same as adding its positive counterpart:
[tex]\[
-10 - (-15) = -10 + 15
\][/tex]
Now, calculate:
[tex]\[
-10 + 15 = 5
\][/tex]
5. Determine if the result is a whole number:
Yes, the result is a whole number because [tex]\(5\)[/tex] is an integer, which is also a whole number.
### Operation on a Number Line:
We can visualize this operation on a number line:
1. Start at [tex]\(-6\)[/tex].
2. Move 4 units left to reach [tex]\(-10\)[/tex].
3. From [tex]\(-10\)[/tex], move 15 units right to reach [tex]\(5\)[/tex].
Here's an approximate representation of the number line:
[tex]\[
\begin{array}{cccccccccccccccccc}
-12 & -11 & -10 & -9 & -8 & -7 & -6 & -5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & \cdots \\
& & & & & \xleftarrow[4]{-6} & & & & & & & & \xrightarrow[15]{-10} & & & & \\
\end{array}
\][/tex]
1. Start at [tex]\(-6\)[/tex], move left 4 units to arrive at [tex]\(-10\)[/tex].
2. From [tex]\(-10\)[/tex], move right 15 units to arrive at [tex]\(5\)[/tex].
### Conclusion:
- The mathematical expression to subtract [tex]\(-15\)[/tex] from the sum of [tex]\(-6\)[/tex] and [tex]\(-4\)[/tex] is:
[tex]\[
(-10) - (-15) = 5
\][/tex]
- The simplified result of this expression is [tex]\(5\)[/tex].
- The result is a whole number because [tex]\(5\)[/tex] is an integer.
- The operation on a number line confirms the steps and the result.
