Certainly! Let's simplify the given expression step by step.
The expression we need to simplify is:
[tex]\[ \frac{1}{4}(8 - 6x + 12) \][/tex]
### Step 1: Distribute [tex]\(\frac{1}{4}\)[/tex] to each term inside the parentheses
We apply the distributive property, which states that [tex]\(a(b + c) = ab + ac\)[/tex].
[tex]\[ \frac{1}{4} \cdot 8 - \frac{1}{4} \cdot 6x + \frac{1}{4} \cdot 12 \][/tex]
### Step 2: Simplify each term individually
- For the first term:
[tex]\[ \frac{1}{4} \cdot 8 = 2 \][/tex]
- For the second term:
[tex]\[ \frac{1}{4} \cdot (-6x) = -\frac{6}{4}x = -\frac{3}{2}x \][/tex]
- For the third term:
[tex]\[ \frac{1}{4} \cdot 12 = 3 \][/tex]
### Step 3: Combine the simplified terms
We add all the simplified terms together:
[tex]\[ 2 - \frac{3}{2}x + 3 \][/tex]
Combine the constants:
[tex]\[ 2 + 3 - \frac{3}{2}x = 5 - \frac{3}{2}x \][/tex]
### Conclusion
The simplified expression is:
[tex]\[ 5 - \frac{3}{2}x \][/tex]
Or equivalently:
[tex]\[ - \frac{3}{2}x + 5 \][/tex]
### Matching with the given options
We compare our result with the given choices:
A. [tex]\(\frac{7}{2} x\)[/tex]
B. [tex]\(-\frac{13}{2} x\)[/tex]
C. [tex]\(-6 x + 14\)[/tex]
D. [tex]\(-\frac{3}{2} x + 5\)[/tex]
The correct answer is:
[tex]\[ \boxed{D} -\frac{3}{2} x + 5 \][/tex]
