Let's go through the multiplication step-by-step and determine whether the solution is reasonable or not.
### Step-by-Step Multiplication
1. Multiply the first two numbers:
- The two numbers are [tex]\(-6\)[/tex] and [tex]\(-7\)[/tex].
- When multiplying two negative numbers, the negatives cancel out, resulting in a positive product.
[tex]\[
(-6) \times (-7) = 42
\][/tex]
2. Multiply the result with the third number:
- Now, take the result from the first multiplication, which is [tex]\(42\)[/tex], and multiply it by [tex]\(-1\)[/tex].
- Multiplying a positive number by a negative number will result in a negative product.
[tex]\[
42 \times (-1) = -42
\][/tex]
### Result
So, the final result of multiplying [tex]\(-6\)[/tex], [tex]\(-7\)[/tex], and [tex]\(-1\)[/tex] together is [tex]\(-42\)[/tex].
### Explanation of Reasonableness
Let's check the reasonableness of the result:
- The product of [tex]\(-6\)[/tex], [tex]\(-7\)[/tex], and [tex]\(-1\)[/tex] is [tex]\(-42\)[/tex].
- Given that we are multiplying three negative numbers, the resulting sign:
- Multiplying two negative numbers gives a positive result.
- Multiplying a positive result with another negative number gives a negative result.
So, the final product must be negative, which matches our result of [tex]\(-42\)[/tex].
### Conclusion
The solution is reasonable since the product of these three numbers, [tex]\(-6\)[/tex], [tex]\(-7\)[/tex], and [tex]\(-1\)[/tex], correctly gives a negative number, [tex]\(-42\)[/tex]. This verification aligns with the rule that multiplying three negative numbers results in a negative product.
