Let's carefully apply the distributive property to the given expression [tex]\(-3(5x - 9) + 4\)[/tex].
### Step-by-Step Solution:
1. Distribute the [tex]\(-3\)[/tex] across the terms within the parentheses:
[tex]\[-3(5x - 9)\][/tex]
2. Perform the multiplication within the parentheses:
- Multiply [tex]\(-3\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[-3 \cdot 5x = -15x\][/tex]
- Multiply [tex]\(-3\)[/tex] by [tex]\(-9\)[/tex]:
[tex]\[-3 \cdot (-9) = 27\][/tex]
3. Combine the results from the multiplication:
[tex]\[-15x + 27\][/tex]
4. Now add the constant [tex]\(4\)[/tex] from the original expression:
[tex]\[-15x + 27 + 4\][/tex]
5. Combine the constants:
[tex]\[27 + 4 = 31\][/tex]
6. This leaves us with:
[tex]\[-15x + 31\][/tex]
### Conclusion:
The simplified expression after applying the distributive property and combining like terms is [tex]\(-15x + 31\)[/tex].
By comparing this with the answer choices provided:
- (A) [tex]\(-15x - 27 + 4\)[/tex]
- (B) [tex]\(-15x - 27 - 12\)[/tex]
- (C) [tex]\(-15x + 27 + 4\)[/tex]
- (D) [tex]\(-15x + 27 - 12\)[/tex]
None of these answer choices match the correct simplification, which is [tex]\(-15x + 31\)[/tex]. Therefore, none of the provided answer choices is correct.
