Certainly! Let's break down the expression step by step to simplify it and find the correct answer.
### Step 1: Simplify the product term
The first part of our expression is [tex]\((-6) \cdot (-3)\)[/tex].
[tex]\[
(-6) \cdot (-3) = 18
\][/tex]
The product of two negative numbers is positive.
### Step 2: Simplify inside the brackets
Next, we deal with the expression inside the brackets: [tex]\([5 - (-3) - (-1) + 4]\)[/tex].
1. Simplify each subtraction of a negative number to an addition:
- Subtracting a negative number is equivalent to adding the positive counterpart.
[tex]\[
5 - (-3) = 5 + 3 = 8
\][/tex]
[tex]\[
8 - (-1) = 8 + 1 = 9
\][/tex]
[tex]\[
9 + 4 = 13
\][/tex]
### Step 3: Add the results
Now we add the simplified results from step 1 and step 2:
[tex]\[
18 + 13 = 31
\][/tex]
### Conclusion
The value of the given expression [tex]\((-6) \cdot (-3) + [5 - (-3) - (-1) + 4]\)[/tex] is [tex]\(31\)[/tex]. Thus, the correct answer is:
[tex]\[
\boxed{31}
\][/tex]
So, the correct choice is:
a. 31
